# Feature Release steps - tests passing - mix format - inline documentation - top of module documentation - OEIS Stats in lib/sequence/oeis.ex - version bump in mix.exs - version bump in README.md - version bump in CHANGELOG - version bump in library.md - update OEIS stats for release version in CHANGELOG - git tag -a v0.x.x -m "v0.x.x - summary" - git push - git push --tags - mix hex.publish # CHANGELOG ## v0.12.0 ``` OEIS Coverage 745 total sequences By Module Elixir.Chunky.Sequence.OEIS - 1 sequences Elixir.Chunky.Sequence.OEIS.Combinatorics - 7 sequences Elixir.Chunky.Sequence.OEIS.Constants - 31 sequences Elixir.Chunky.Sequence.OEIS.Core - 136 sequences Elixir.Chunky.Sequence.OEIS.Factors - 122 sequences Elixir.Chunky.Sequence.OEIS.Multiples - 75 sequences Elixir.Chunky.Sequence.OEIS.Powers - 48 sequences Elixir.Chunky.Sequence.OEIS.Primes - 100 sequences Elixir.Chunky.Sequence.OEIS.Repr - 205 sequences Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences Sequence Groups OEIS Core Sequences - 135 / 177 (76.27%) OEIS Core::Easy Sequences - 121 / 146 (82.88%) OEIS Core::Hard Sequences - 12 / 12 (100.0%) OEIS Core::Multiplicative Sequences - 22 / 22 (100.0%) OEIS Core::Eigen Sequences - 5 / 5 (100.0%) ``` ### Enhancements - Chunky.Math - refactored nth_root_int/2 into: - nth_integer_root/2 -> {:exact, __} or {:nearest, __} - nth_integer_root!/2 -> val - reduced_prime_factors/1 - has_subset_sum?/2 - is_narcissistic_in_base?/2 - new module Chunky.Math.Predicates - refactored all functions of form `is_*?/1` from Chunky.Math to Chunky.Math.Predicates - Math.Predicates - is_singly_even_number?/1 - is_doubly_even_number?/1 - is_economical_number?/1 - is_wasteful_number?/1 - is_equidigital_number?/1 - is_happy_number?/1 - is_unhappy_number?/1 - is_evil_number?/1 - is_polite_number?/1 - is_impolite_number?/1 - is_smith_number?/1 - is_hoax_number?/1 - is_nonhypotenuse_number?/1 - is_hypotenuse_number?/1 - is_practical_number?/1 - is_primary_pseudoperfect_number?/1 - is_pseudoperfect_number?/1 - is_erdos_nicolas_number?/1 - is_weird_number?/11 - is_primitive_pseudoperfect_number?/1 - is_primitive_weird_number?/1 - is_semiprime_number?/1 - is_squarefree_semiprime?/1 - is_kaprekar_number?/1 - is_kaprekar_strict_number?/1 - is_narcissistic_number?/1 - is_munchhausen_number?/1 - is_harshad_number?/1 - is_moran_number?/1 - is_zuckerman_number?/1 - is_apocalypse_number?/1 - is_apocalypse_prime?/1 - is_beast_number?/1 ### Sequences - Passed 75% coverage of OEIS Core sequences - A016825 - Positive integers congruent to 2 mod 4 - A046759 - Economical numbers - A046760 - Wasteful numbers - A046758 - Equidigital numbers - A007770 - Happy numbers - A031177 - Unhappy numbers - A057716 - The non-powers of 2 - A138591 - Sums of two or more consecutive nonnegative integers - A006753 - Smith (or joke) numbers - A019506 - Hoax numbers - A004144 - Nonhypotenuse numbers - A009003 - Hypotenuse numbers - A005153 - Practical numbers - A054377 - Primary pseudoperfect numbers - A005835 - Pseudoperfect (or semiperfect) numbers - A194472 - Erdős-Nicolas numbers - A006037 - Weird numbers - A006036 - Primitive pseudoperfect numbers - A002975 - Primitive weird numbers - A006886 - Kaprekar numbers - A053816 - Another version of the Kaprekar numbers - A005188 - Armstrong (or pluperfect, or Plus Perfect, or narcissistic) numbers - A010353 - Base-9 Armstrong or narcissistic numbers - A010354 - Base-8 Armstrong or narcissistic numbers - A010350 - Base-7 Armstrong or narcissistic numbers - A010348 - Base-6 Armstrong or narcissistic numbers - A010346 - Base-5 Armstrong or narcissistic numbers - A010344 - Base-4 Armstrong or narcissistic numbers - A161948 - Base-11 Armstrong or narcissistic numbers - A161949 - Base-12 Armstrong or narcissistic numbers - A161950 - Base-13 Armstrong or narcissistic numbers - A161951 - Base-14 Armstrong or narcissistic numbers - A161952 - Base-15 Armstrong or narcissistic numbers - A161953 - Base-16 Armstrong or narcissistic numbers - A114904 - Sorted numbers of digits of any base-10 narcissistic number - A014576 - Smallest n-digit narcissistic (or Armstrong) number - A046253 - Equal to the sum of its nonzero digits raised to its own power - A001101 - Moran numbers: n such that (n / sum of digits of n) is prime - A005349 - Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits - A007602 - Numbers that are divisible by the product of their digits - A115983 - Apocalypse primes: 10^665+a(n) has 666 decimal digits and is prime - A051003 - Beastly (or hateful) numbers: numbers containing the string 666 in their decimal expansion ## v0.11.5 ``` OEIS Coverage 703 total sequences By Module Elixir.Chunky.Sequence.OEIS - 1 sequences Elixir.Chunky.Sequence.OEIS.Combinatorics - 7 sequences Elixir.Chunky.Sequence.OEIS.Constants - 31 sequences Elixir.Chunky.Sequence.OEIS.Core - 136 sequences Elixir.Chunky.Sequence.OEIS.Factors - 119 sequences Elixir.Chunky.Sequence.OEIS.Multiples - 60 sequences Elixir.Chunky.Sequence.OEIS.Powers - 47 sequences Elixir.Chunky.Sequence.OEIS.Primes - 100 sequences Elixir.Chunky.Sequence.OEIS.Repr - 182 sequences Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences Sequence Groups OEIS Core Sequences - 135 / 177 (76.27%) OEIS Core::Easy Sequences - 121 / 146 (82.88%) OEIS Core::Hard Sequences - 12 / 12 (100.0%) OEIS Core::Multiplicative Sequences - 22 / 22 (100.0%) OEIS Core::Eigen Sequences - 5 / 5 (100.0%) ``` - Math - double_factorial/1 - repunit/1 - stern_diatomic_series/1 - n_choose_k/2 - stirling_partition_number/2 - schroder_number/1 - chebyshev_triangle_coefficient/2 - bernoulli_number/1 - two_color_bracelet_with_period_count/2 - two_color_bracelet_count/2 - binary_partitions_count/1 - nth_root_int/2 - total_partitions/1 - ordered_factorization_count/1 - is_repunit?/1 - is_repdigit?/1 - is_cyclops_number_in_base?/2 - is_cyclops_number?/1 - perfect_partition_count/1 - digit_runs/2 - digit_runs_count/2 - planted_3_trees_count/1 - Sequences - A001567 - Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers. - A005935 - Pseudoprimes to base 3. - A005936 - Pseudoprimes to base 5. - A005937 - Pseudoprimes to base 6. - A005938 - Pseudoprimes to base 7. - A005939 - Pseudoprimes to base 10. - A020136 - Fermat pseudoprimes to base 4. - A020137 - Pseudoprimes to base 8. - A020138 - Pseudoprimes to base 9. - A020139 - Pseudoprimes to base 11. - A020140 - Pseudoprimes to base 12. - A020141 - Pseudoprimes to base 13. - A020142 - Pseudoprimes to base 14. - A020143 - Pseudoprimes to base 15. - A020144 - Pseudoprimes to base 16. - A020145 - Pseudoprimes to base 17. - A020146 - Pseudoprimes to base 18. - A020147 - Pseudoprimes to base 19. - A020148 - Pseudoprimes to base 20. - A020149 - Pseudoprimes to base 21. - A020150 - Pseudoprimes to base 22. - A020151 - Pseudoprimes to base 23. - A020152 - Pseudoprimes to base 24. - A020153 - Pseudoprimes to base 25. - A020154 - Pseudoprimes to base 26. - A020155 - Pseudoprimes to base 27. - A020156 - Pseudoprimes to base 28. - A020157 - Pseudoprimes to base 29. - A020158 - Pseudoprimes to base 30. - A020159 - Pseudoprimes to base 31. - A020160 - Pseudoprimes to base 32. - A020161 - Pseudoprimes to base 33. - A020162 - Pseudoprimes to base 34. - A020163 - Pseudoprimes to base 35. - A020164 - Pseudoprimes to base 36. - A020165 - Pseudoprimes to base 37. - A020166 - Pseudoprimes to base 38. - A020167 - Pseudoprimes to base 39. - A020168 - Pseudoprimes to base 40. - A020169 - Pseudoprimes to base 41. - A020170 - Pseudoprimes to base 42. - A020171 - Pseudoprimes to base 43. - A020172 - Pseudoprimes to base 44. - A020173 - Pseudoprimes to base 45. - A020174 - Pseudoprimes to base 46. - A020175 - Pseudoprimes to base 47. - A020176 - Pseudoprimes to base 48. - A020177 - Pseudoprimes to base 49. - A020178 - Pseudoprimes to base 50. - A020179 - Pseudoprimes to base 51. - A020180 - Pseudoprimes to base 52. - A020181 - Pseudoprimes to base 53. - A020182 - Pseudoprimes to base 54. - A020183 - Pseudoprimes to base 55. - A020184 - Pseudoprimes to base 56. - A020185 - Pseudoprimes to base 57. - A020186 - Pseudoprimes to base 58. - A020187 - Pseudoprimes to base 59. - A020188 - Pseudoprimes to base 60. - A020189 - Pseudoprimes to base 61. - A020190 - Pseudoprimes to base 62. - A020191 - Pseudoprimes to base 63. - A020192 - Pseudoprimes to base 64. - A020193 - Pseudoprimes to base 65. - A020194 - Pseudoprimes to base 66. - A020195 - Pseudoprimes to base 67. - A020196 - Pseudoprimes to base 68. - A020197 - Pseudoprimes to base 69. - A020198 - Pseudoprimes to base 70. - A020199 - Pseudoprimes to base 71. - A020200 - Pseudoprimes to base 72. - A020201 - Pseudoprimes to base 73. - A020202 - Pseudoprimes to base 74. - A020203 - Pseudoprimes to base 75. - A020204 - Pseudoprimes to base 76. - A020205 - Pseudoprimes to base 77. - A020206 - Pseudoprimes to base 78. - A020207 - Pseudoprimes to base 79. - A020208 - Pseudoprimes to base 80. - A020209 - Pseudoprimes to base 81. - A020210 - Pseudoprimes to base 82. - A020211 - Pseudoprimes to base 83. - A020212 - Pseudoprimes to base 84. - A020213 - Pseudoprimes to base 85. - A020214 - Pseudoprimes to base 86. - A020215 - Pseudoprimes to base 87. - A020216 - Pseudoprimes to base 88. - A020217 - Pseudoprimes to base 89. - A020218 - Pseudoprimes to base 90. - A020219 - Pseudoprimes to base 91. - A020220 - Pseudoprimes to base 92. - A020221 - Pseudoprimes to base 93. - A020222 - Pseudoprimes to base 94. - A020223 - Pseudoprimes to base 95. - A020224 - Pseudoprimes to base 96. - A020225 - Pseudoprimes to base 97. - A020226 - Pseudoprimes to base 98. - A020227 - Pseudoprimes to base 99. - A020228 - Pseudoprimes to base 100. - A001147 - Double factorial of odd numbers: a(n) = (2*n-1)!! = 1*3*5*...*(2*n-1). - A001405 - a(n) = binomial(n, floor(n/2)). - A001519 - a(n) = 3*a(n-1) - a(n-2), with a(0) = a(1) = 1. - A001700 - a(n) = binomial(2n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1. - A001764 - a(n) = binomial(3n,n)/(2n+1) (enumerates ternary trees and also noncrossing trees). - A006882 - Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1 - A001906 - F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2). - A001969 - Evil numbers: numbers with an even number of 1's in their binary expansion. - A002113 - Palindromes in base 10. - A002275 - Repunits: (10^n - 1)/9. Often denoted by R_n. - A002378 - Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1). - A002487 - Stern's diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2*n) = a(n), a(2*n+1) = a(n) + a(n+1). - A002620 - Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4). - A003418 - Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1. - A004526 - Nonnegative integers repeated, floor(n/2). - A005408 - The odd numbers: a(n) = 2*n + 1. - A006318 - Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers). - A007318 - Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n. - A008277 - Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n. - A018252 - The nonprime numbers: 1 together with the composite numbers, A002808. - A027642 - Denominator of Bernoulli number B_n. - A049310 - Triangle of coefficients of Chebyshev's S(n,x) := U(n,x/2) polynomials (exponents in increasing order). - A070939 - Length of binary representation of n. - A000029 - Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets). - A000031 - Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n. - A000048 - Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged. - A000123 - Number of binary partitions: number of partitions of 2n into powers of 2. - A000161 - Number of partitions of n into 2 squares. - A000311 - Schroeder's fourth problem; also series-reduced rooted trees with n labeled leaves; also number of total partitions of n. - A001478 - The negative integers. - A002531 - a(2*n) = a(2*n-1) + a(2*n-2), a(2*n+1) = 2*a(2*n) + a(2*n-1); a(0) = a(1) = 1. - A074206 - Kalmár's [Kalmar's] problem: number of ordered factorizations of n. - A001057 - Canonical enumeration of integers: interleaved positive and negative integers with zero prepended - A001333 - Numerators of continued fraction convergents to sqrt(2). - A001481 - Numbers that are the sum of 2 squares. - A001699 - Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative. - A002033 - Number of perfect partitions of n. - A002110 - Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#. - A002530 - a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1. - A005588 - Number of free binary trees admitting height n. - A005811 - Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n. - A006894 - Number of planted 3-trees of height < n. - A008279 - Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time. ## v0.11.4 ### Enhancements - New module Chunky.Math.Operations - summation/3 macro - product/3 macro - Math - is_vampire_number?/1 - is_double_vampire_number?/1 - is_prime_vampire_number?/1 - factor_pairs/2 - is_in_base?/2 - length_in_base/2 - is_pseudo_vampire_number?/1 - is_pandigital?/1 - is_pandigital_in_base?/2 - is_left_truncatable_prime?/1 - is_right_truncatable_prime?/1 - is_left_right_truncatable_prime?/1 - is_two_sided_prime?/1 - is_palindromic_prime?1 - is_emirp_prme?/1 - is_circular_prime?/1 - is_weakly_prime?/1 - rotations/1 - reverse_number/1 - is_palindromic?/1 - is_palindromic_in_base?/2 - is_strictly_non_palindromic?/1 - is_carmichael_number?/1 - is_euler_jacobi_pseudo_prime?/1 - is_euler_pseudo_prime?/1 - is_poulet_number?/1 - is_pseudo_prime?/1 - coprimes/1 - coprimes/2 - is_euler_jacobi_pseudo_prime?/2 - is_euler_pseudo_prime?/2 - is_pseudo_prime?/2 - jacobi_symbol/2 - legendre_symbol/2 - to_base/2 now supports any base > 1 ## v0.11.3 ``` OEIS Coverage 561 total sequences By Module Elixir.Chunky.Sequence.OEIS - 1 sequences Elixir.Chunky.Sequence.OEIS.Combinatorics - 7 sequences Elixir.Chunky.Sequence.OEIS.Constants - 31 sequences Elixir.Chunky.Sequence.OEIS.Core - 93 sequences Elixir.Chunky.Sequence.OEIS.Factors - 119 sequences Elixir.Chunky.Sequence.OEIS.Multiples - 60 sequences Elixir.Chunky.Sequence.OEIS.Powers - 47 sequences Elixir.Chunky.Sequence.OEIS.Primes - 1 sequences Elixir.Chunky.Sequence.OEIS.Repr - 182 sequences Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences Sequence Groups OEIS Core Sequences - 92 / 177 (51.98%) OEIS Core::Easy Sequences - 78 / 146 (53.42%) OEIS Core::Hard Sequences - 12 / 12 (100.0%) OEIS Core::Multiplicative Sequences - 22 / 22 (100.0%) OEIS Core::Eigen Sequences - 5 / 5 (100.0%) ``` ### Enhancements - Fractions - power/3 now handles coercion values for string, int, and float - fixed reducable values not having proper fractional results (previously returned :no_fractional_power) - Added absolute_value/1 - Added near_equal?/3 - Added floor/1 and ceiling/1 - Added increment/2 and decrement/2 - increment/2 and decrement/2 support `:both` option - Added within?/3 and within?/2 - added type guard: is_coercible? - all new fraction functions from this release support type coercion (using is_coercible?/1) - added round/1 for rounding to nearest whole value - Sequence - added `start/1` function as alias to `next!/1` - added `restart/1` function - added `at/2` similar to Enum.at - added `create/1` to initialize a new sequence from a description bundle. - Sequence.OEIS - added `find_sequence/1`, `find_sequence!/1`, and `has_sequence?/1` - new module Chunky.Timeout - macro: with_timeout/2 - Math - digit_sum/1 - contains_digit?/2 - remove_digits!/2 - is_rhonda_to_base?/2 - get_rhonda_to/2 - is_rhonda_to_base_*?/1 - is_multiple_rhonda?/1 - to_base/2 - digit_count/3 - is_plaindrome?/1 - is_plaindrome_in_base?/2 ### Sequences - Added new sequence module OEIS.Powers - Added new sequence module OEIS.Repr - Added new sequence module OEIS.Combinatorics - New Sequences - A000051 - a(n) = 2^n + 1 - A000351 - a(n) = 5^n - A000400 - a(n) = 6^n - A000420 - a(n) = 7^n - A001018 - a(n) = 8^n - A001019 - a(n) = 9^n - A011557 - a(n) = 10^n - A001020 - a(n) = 11^n - A001021 - a(n) = 12^n - A001022 - a(n) = 13^n - A001023 - a(n) = 14^n - A001024 - Powers of 15. - A001025 - Powers of 16: a(n) = 16^n. - A001026 - Powers of 17. - A001027 - Powers of 18. - A001029 - Powers of 19. - A009964 - Powers of 20. - A009965 - Powers of 21. - A009966 - Powers of 22. - A009967 - Powers of 23. - A009968 - Powers of 24: a(n) = 24^n. - A009969 - Powers of 25. - A009970 - Powers of 26. - A009971 - Powers of 27. - A009972 - Powers of 28. - A009973 - Powers of 29. - A009974 - Powers of 30. - A009975 - Powers of 31. - A009976 - Powers of 32. - A009977 - Powers of 33. - A009978 - Powers of 34. - A009979 - Powers of 35. - A009980 - Powers of 36. - A009981 - Powers of 37. - A009982 - Powers of 38. - A009983 - Powers of 39. - A009984 - Powers of 40. - A009985 - Powers of 41. - A009986 - Powers of 42. - A009987 - Powers of 43. - A009988 - Powers of 44. - A009989 - Powers of 45. - A009990 - Powers of 46. - A009991 - Powers of 47. - A009992 - Powers of 48: a(n) = 48^n. - A008585 - a(n) = 3*n. - A008586 - Multiples of 4. - A008587 - Multiples of 5. - A008588 - Nonnegative multiples of 6. - A008589 - Multiples of 7. - A008590 - Multiples of 8. - A008591 - Multiples of 9. - A008592 - Multiples of 10: a(n) = 10 * n. - A008593 - Multiples of 11. - A008594 - Multiples of 12. - A008595 - Multiples of 13. - A008596 - Multiples of 14. - A008597 - Multiples of 15. - A008598 - Multiples of 16. - A008599 - Multiples of 17. - A008600 - Multiples of 18. - A008601 - Multiples of 19. - A008602 - Multiples of 20. - A008603 - Multiples of 21. - A008604 - Multiples of 22. - A008605 - Multiples of 23. - A008606 - Multiples of 24. - A008607 - Multiples of 25. - A005843 - The nonnegative even numbers: a(n) = 2n. - A087752 - Powers of 49. - A159991 - Powers of 60. - A169823 - Multiples of 60. - A169825 - Multiples of 420. - A169827 - Multiples of 840. - A018253 - Divisors of 24. - A018256 - Divisors of 36. - A018261 - Divisors of 48. - A018266 - Divisors of 60. - A018293 - Divisors of 120. - A018321 - Divisors of 180. - A018350 - Divisors of 240. - A018412 - Divisors of 360. - A018609 - Divisors of 720. - A018676 - Divisors of 840. - A165412 - Divisors of 2520. - A178858 - Divisors of 5040. - A178859 - Divisors of 7560. - A178860 - Divisors of 10080. - A178861 - Divisors of 15120. - A178862 - Divisors of 20160. - A178863 - Divisors of 25200. - A178864 - Divisors of 27720. - A178877 - Divisors of 1260. - A178878 - Divisors of 1680. - A252994 - Multiples of 26. - A305548 - a(n) = 27*n. - A135628 - Multiples of 28. - A195819 - Multiples of 29. - A249674 - a(n) = 30*n. - A135631 - Multiples of 31. - A174312 - 32*n. - A044102 - Multiples of 36. - A085959 - Multiples of 37. - A152691 - Multiples of 64. - A121023 - Multiples of 3 containing a 3 in their decimal representation. - A121024 - Multiples of 4 containing a 4 in their decimal representation. - A121025 - Multiples of 5 containing a 5 in their decimal representation. - A121026 - Multiples of 6 containing a 6 in their decimal representation. - A121027 - Multiples of 7 containing a 7 in their decimal representation. - A121028 - Multiples of 8 containing an 8 in their decimal representation. - A121029 - Multiples of 9 containing a 9 in their decimal representation. - A121030 - Multiples of 10 containing a 10 in their decimal representation. - A121031 - Multiples of 11 containing an 11 in their decimal representation. - A121032 - Multiples of 12 containing a 12 in their decimal representation. - A121033 - Multiples of 13 containing a 13 in their decimal representation. - A121034 - Multiples of 14 containing a 14 in their decimal representation. - A121035 - Multiples of 15 containing a 15 in their decimal representation. - A121036 - Multiples of 16 containing a 16 in their decimal representation. - A121037 - Multiples of 17 containing a 17 in their decimal representation. - A121038 - Multiples of 18 containing a 18 in their decimal representation. - A121039 - Multiples of 19 containing a 19 in their decimal representation. - A121040 - Multiples of 20 containing a 20 in their decimal representation. - A062768 - Multiples of 6 such that the sum of the digits is equal to 6. - A063416 - Multiples of 7 whose sum of digits is equal to 7. - A063997 - Multiples of 4 whose digits add to 4. - A069537 - Multiples of 2 with digit sum = 2. - A069540 - Multiples of 5 with digit sum 5. - A069543 - Multiples of 8 with digit sum 8. - A011531 - Numbers that contain a digit 1 in their decimal representation. - A011532 - Numbers that contain a 2. - A011533 - Numbers that contain a 3. - A011534 - Numbers that contain a 4. - A011535 - Numbers that contain a 5. - A011536 - Numbers that contain a 6. - A011537 - Numbers that contain at least one 7. - A011538 - Numbers that contain an 8. - A011539 - "9ish numbers": decimal representation contains at least one nine. - A011540 - Numbers that contain a digit 0. - A007395 - Constant sequence: the all 2's sequence. - A010701 - Constant sequence: the all 3's sequence. - A010709 - Constant sequence: the all 4's sequence. - A010716 - Constant sequence: the all 5's sequence. - A010722 - Constant sequence: the all 6's sequence. - A010727 - Constant sequence: the all 7's sequence. - A010731 - Constant sequence: the all 8's sequence. - A010734 - Constant sequence: the all 9's sequence. - A010692 - Constant sequence: a(n) = 10. - A010850 - Constant sequence: a(n) = 11. - A010851 - Constant sequence: a(n) = 12. - A010852 - Constant sequence: a(n) = 13. - A010853 - Constant sequence: a(n) = 14. - A010854 - Constant sequence: a(n) = 15. - A010855 - Constant sequence: a(n) = 16. - A010856 - Constant sequence: a(n) = 17. - A010857 - Constant sequence: a(n) = 18. - A010858 - Constant sequence: a(n) = 19. - A010859 - Constant sequence: a(n) = 20. - A010860 - Constant sequence: a(n) = 21. - A010861 - Constant sequence: a(n) = 22. - A010862 - Constant sequence: a(n) = 23. - A010863 - Constant sequence: a(n) = 24. - A010864 - Constant sequence: a(n) = 25. - A010865 - Constant sequence: a(n) = 26. - A010866 - Constant sequence: a(n) = 27. - A010867 - Constant sequence: a(n) = 28. - A010868 - Constant sequence: a(n) = 29. - A010869 - Constant sequence: a(n) = 30. - A010870 - Constant sequence: a(n) = 31. - A010871 - Constant sequence: a(n) = 32. - A052382 - Numbers without 0 as a digit, a.k.a. zeroless numbers. - A052383 - Numbers without 1 as a digit. - A052404 - Numbers without 2 as a digit. - A052405 - Numbers without 3 as a digit. - A052406 - Numbers without 4 as a digit. - A052413 - Numbers without 5 as a digit. - A052414 - Numbers without 6 as a digit. - A052419 - Numbers without 7 as a digit. - A052421 - Numbers without 8 as a digit. - A004176 - Omit 1's from n. - A004177 - Omit 2's from n. - A004178 - Omit 3's from n. - A004179 - Omit 4's from n. - A004180 - Omit 5's from n. - A004181 - Omit 6's from n. - A004182 - Omit 7's from n. - A004183 - Omit 8's from n. - A004184 - Omit 9's from n. - A004719 - Delete all 0's from n. - A004720 - Delete all digits '1' from the sequence of nonnegative integers. - A004721 - Delete all 2's from the sequence of nonnegative integers. - A004722 - Delete all digits 3 from the terms of the sequence of nonnegative integers. - A004723 - Delete all 4's from the sequence of nonnegative integers. - A004724 - Delete all 5's from the sequence of nonnegative integers. - A004725 - Delete all 6's from the sequence of nonnegative integers. - A004726 - Delete all 7's from the sequence of nonnegative integers. - A004727 - Delete all 8's from the sequence of nonnegative integers. - A004728 - Delete all 9's from the sequence of nonnegative integers. - A007088 - The binary numbers (or binary words, or binary vectors): numbers written in base 2. - A007089 - Numbers in base 3. - A007090 - Numbers in base 4. - A007091 - Numbers in base 5. - A007092 - Numbers in base 6. - A007093 - Numbers in base 7. - A007094 - Numbers in base 8. - A007095 - Numbers in base 9. - A121022 - Even numbers containing a 2 in their decimal representation. - A100968 - Integers n that are Rhonda numbers to base 4. - A100969 - Integers n that are Rhonda numbers to base 6. - A100970 - Integers n that are Rhonda numbers to base 8. - A100973 - Integers that are Rhonda numbers to base 9. - A099542 - Rhonda numbers to base 10. - A100971 - Integers n that are Rhonda numbers to base 12. - A100972 - Integers that are Rhonda numbers to base 14. - A100974 - Integers that are Rhonda numbers to base 15. - A100975 - Integers that are Rhonda numbers to base 16. - A255732 - Rhonda numbers in vigesimal number system. - A255736 - Integers that are Rhonda numbers to base 30. - A255731 - Rhonda numbers in sexagesimal number system. - A100988 - Integers that are Rhonda numbers to more than one base. - A100987 - Integers that are Rhonda numbers to some base. - A159981 - Catalan numbers read modulo 4 . - A159984 - Catalan numbers read modulo 5 . - A159986 - Catalan numbers read modulo 7 . - A159987 - Catalan numbers read modulo 8. - A159988 - Catalan numbers read modulo 11 . - A159989 - Catalan numbers read modulo 12. - A289682 - Catalan numbers read modulo 16. - A002808 - The composite numbers: numbers n of the form x*y for x > 1 and y > 1. - A255735 - Integers that are Rhonda numbers to base 18. - A000788 - Total number of 1's in binary expansions of 0, ..., n. - A005823 - Numbers whose ternary expansion contains no 1's. - A005836 - Numbers n whose base 3 representation contains no 2. - A007954 - Product of decimal digits of n. - A010872 - a(n) = n mod 3. - A023416 - Number of 0's in binary expansion of n. - A023705 - Numbers with no 0's in base 4 expansion. - A032924 - Numbers whose ternary expansion contains no 0. - A052040 - Numbers n such that n^2 lacks the digit zero in its decimal expansion. - A055640 - Number of nonzero digits in decimal expansion of n. - A055641 - Number of zero digits in n. - A055642 - Number of digits in decimal expansion of n. - A067251 - Numbers with no trailing zeros in decimal representation. - A071858 - (Number of 1's in binary expansion of n) mod 3. - A122840 - a(n) is the number of 0s at the end of n when n is written in base 10. - A160093 - Number of digits in n, excluding any trailing zeros. - A179868 - (Number of 1's in binary expansion of n) mod 4. - A193238 - Number of prime digits in decimal representation of n. - A196563 - Number of even digits in decimal representation of n. - A248910 - Numbers with no zeros in base-6 representation. - A255805 - Numbers with no zeros in base-8 representation. - A255808 - Numbers with no zeros in base-9 representation. - A001414 - Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n). - A001489 - a(n) = -n. - A007953 - Digital sum (i.e., sum of digits) of n; also called digsum(n). - A014263 - Numbers that contain even digits only. - A023692 - Numbers with a single 1 in their ternary expansion. - A023693 - Numbers with exactly 2 1's in ternary expansion. - A023694 - Numbers with exactly 3 1's in ternary expansion. - A023695 - Numbers with exactly 4 1's in ternary expansion. - A023696 - Numbers with exactly 5 1's in ternary expansion. - A023697 - Numbers with exactly 6 1's in ternary expansion. - A043321 - Numbers n such that number of 0's in base 3 is 1. - A059015 - Total number of 0's in binary expansions of 0, ..., n. - A062756 - Number of 1's in ternary (base 3) expansion of n. - A074940 - Numbers having at least one 2 in their ternary representation. - A077267 - Number of zeros in base 3 expansion of n. - A081603 - Number of 2's in ternary representation of n. - A081605 - Numbers having at least one 0 in their ternary representation. - A081606 - Numbers having at least one 1 in their ternary representation. - A097251 - Numbers whose set of base 5 digits is {0,4}. - A097252 - Numbers whose set of base 6 digits is {0,5}. - A097253 - Numbers whose set of base 7 digits is {0,6}. - A097254 - Numbers whose set of base 8 digits is {0,7}. - A097255 - Numbers whose set of base 9 digits is {0,8}. - A097256 - Numbers whose set of base 10 digits is {0,9}. - A097257 - Numbers whose set of base 11 digits is {0,A}, where A base 11 = 10 base 10. - A097258 - Numbers whose set of base 12 digits is {0,B}, where B base 12 = 11 base 10. - A097259 - Numbers whose set of base 13 digits is {0,C}, where C base 13 = 12 base 10. - A097260 - Numbers whose set of base 14 digits is {0,D}, where D base 14 = 13 base 10. - A097261 - Numbers whose set of base 15 digits is {0,E}, where E base 15 = 14 base 10. - A097262 - Numbers whose set of base 16 digits is {0,F}, where F base 16 = 15 base 10. - A102669 - Number of digits >= 2 in decimal representation of n. - A102670 - Number of digits >= 2 in the decimal representations of all integers from 0 to n. - A102671 - Number of digits >= 3 in decimal representation of n. - A102672 - Number of digits >= 3 in the decimal representations of all integers from 0 to n. - A102673 - Number of digits >= 4 in decimal representation of n. - A102674 - Number of digits >= 4 in the decimal representations of all integers from 0 to n. - A102675 - Number of digits >= 5 in decimal representation of n. - A102676 - Number of digits >= 5 in the decimal representations of all integers from 0 to n. - A102677 - Number of digits >= 6 in decimal representation of n. - A102678 - Number of digits >= 6 in the decimal representations of all integers from 0 to n. - A102679 - Number of digits >= 7 in decimal representation of n. - A102680 - Number of digits >= 7 in the decimal representations of all integers from 0 to n. - A102681 - Number of digits >= 8 in decimal representation of n. - A102682 - Number of digits >= 8 in the decimal representations of all integers from 0 to n. - A102683 - Number of digits 9 in decimal representation of n. - A102684 - Number of times the digit 9 appears in the decimal representations of all integers from 0 to n. - A023698 - Numbers with exactly 7 1's in ternary expansion. - A023699 - Numbers with a single 2 in their ternary expansion. - A023700 - Numbers with exactly 2 2's in ternary expansion. - A023701 - Numbers with exactly 3 2's in their ternary expansion. - A023702 - Numbers with exactly 4 2's in ternary expansion of n. - A023703 - Numbers with exactly 5 2's in ternary expansion. - A023704 - Numbers with exactly 6 2's in ternary expansion. - A023706 - Numbers with a single 0 in their base 4 expansion. - A023707 - Numbers with exactly 2 0's in base 4 expansion. - A023708 - Numbers with exactly 3 0's in base 4 expansion. - A023709 - Numbers with no 1's in base 4 expansion. - A023710 - Numbers with a single 1 in their base 4 expansion. - A023711 - Numbers with exactly 2 1's in base 4 expansion. - A023712 - Numbers with exactly 3 1's in base 4 expansion. - A023713 - Numbers with no 2's in base 4 expansion. - A023714 - Numbers with a single 2 in their base 4 expansion. - A023715 - Numbers with exactly 2 2's in base 4 expansion. - A023716 - Numbers with exactly 3 2's in base 4 expansion. - A023717 - Numbers with no 3's in base 4 expansion. - A023718 - Numbers with a single 3 in their base 4 expansion. - A023719 - Numbers with exactly two 3's in base 4 expansion. - A023720 - Numbers with exactly 3 3's in base 4 expansion. - A023721 - Numbers with no 0's in their base-5 expansion. - A023722 - Numbers with a single 0 in their base 5 expansion. - A023723 - Numbers with exactly 2 0's in base 5 expansion. - A023724 - Numbers with exactly 3 0's in base 5 expansion. - A023725 - Numbers with no 1's in their base-5 expansion. - A023726 - Numbers with a single 1 in their base 5 expansion. - A023727 - Numbers with exactly 2 1's in their base 5 expansion. - A023728 - Numbers with exactly 3 1's in base 5 expansion. - A023729 - Numbers with no 2's in their base-5 expansion. - A023730 - Numbers with a single 2 in their base 5 expansion. - A023731 - Numbers with exactly two 2's in base 5 expansion. - A023732 - Numbers with exactly 3 2's in base 5 expansion. - A023733 - Numbers with no 3's in base-5 expansion. - A023734 - Numbers with a single 3 in their base-5 expansion. - A023735 - Numbers with exactly 2 3's in their base-5 expansion. - A023736 - Numbers with exactly 3 3's in their base-5 expansion. - A023738 - Numbers with a single 4 in their base 5 expansion. - A023739 - Numbers with exactly 2 4's in base 5 expansion. - A023740 - Numbers with exactly 3 4's in base 5 expansion. - A023745 - Plaindromes: numbers whose digits in base 3 are in nondecreasing order. - A023746 - Plaindromes: numbers whose digits in base 4 are in nondecreasing order. - A023747 - Plaindromes: numbers whose digits in base 5 are in nondecreasing order. - A023748 - Plaindromes: numbers whose digits in base 6 are in nondecreasing order. - A023749 - Plaindromes: numbers whose digits in base 7 are in nondecreasing order. - A023750 - Plaindromes: numbers whose digits in base 8 are in nondecreasing order. - A023751 - Plaindromes: numbers whose digits in base 9 are in nondecreasing order. - A023752 - Plaindromes: numbers whose digits in base 11 are in nondecreasing order. - A023753 - Plaindromes: numbers whose digits in base 12 are in nondecreasing order. - A023754 - Plaindromes: numbers whose digits in base 13 are in nondecreasing order. - A023755 - Plaindromes: numbers whose digits in base 14 are in nondecreasing order. - A023756 - Plaindromes: numbers whose digits in base 15 are in nondecreasing order. - A023757 - Plaindromes: numbers whose digits in base 16 are in nondecreasing order. ## v0.11.2 ### Build/Development changes - Module requiring HTTPoison and Jason excluded from packaging - HTTPoison and Jason moved to `dev` and `test` only requirements - Credo is now being used for style/consistency checks (with specific configuration to make credo run in a reasonable time frame) - new documentation as main page for hexdocs (library.md) ### Libraries - Refactored Fractions.lcm/1 and Fractions.lcm/2 to Math.lcm/1 and Math.lcm/2 - Refactored nth_root/3, integer_nth_root?/3, and floats_equal?/3 from Fractions to Math - Updated all cached Math functions to use CacheAgent.cache_as macro ### Sequences - Moved A000045/Fibonacci from Sequence.OEIS to Sequence.OEIS.Core ## v0.11.1 ### Enhancements - Chunky.Math - `analyze_number/2` - Run all predicates against `n` to generate labels for `n` - `is_odd?/1` - New predicate - `is_even?/1` - New predicate - `is_zero?/1` - New predicate - `is_positive?/1` - New predicate - `is_negative?/1` - New predicate - all predicates of form `is_*?/1` now work for all integers in range `(-∞..+∞) ## v0.11.0 ``` OEIS Coverage 210 total sequences By Module Elixir.Chunky.Sequence.OEIS - 3 sequences Elixir.Chunky.Sequence.OEIS.Core - 88 sequences Elixir.Chunky.Sequence.OEIS.Factors - 98 sequences Elixir.Chunky.Sequence.OEIS.Primes - 1 sequences Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences Sequence Groups OEIS Core Sequences - 89 / 177 (50.28%) OEIS Core::Easy Sequences - 75 / 146 (51.37%) OEIS Core::Hard Sequences - 12 / 12 (100.0%) OEIS Core::Multiplicative Sequences - 22 / 22 (100.0%) OEIS Core::Eigen Sequences - 5 / 5 (100.0%) ``` ### Enhancements - added Chunky.CacheAgent - caching agent for particularly recursive functions - Chunky.Math - ramanujan_tau/1 - Find the ramanujan tau error value for `n` - partition_count/1 - Recursive (and cached) Partition Function for `n` - abelian_group_count/1 - Number of Abelian groups of order `n` - p_adic_valuation/2 - The _p-adic_ valuation function (for prime `p` and integer `n`) - rooted_tree_count/1 - Rooted trees of N nodes - is_of_form_mx_plus_b/3 - Does number have form `mx + b` for strict values of `m` and `b`? - divisors_of_form_mx_plus_b/3 - Find divisors of `n` that are of form `mx + b` - hurwitz_radon_number/1 - find the hurwitz-radon number of `n` - catalan_number/1 - Find `C(n)`, the Catalan number, of `n` - euler_zig_zag/1 - Permutation set sizes - factorial/1 - Factorial `n!` - binomial/2 - Binomial coefficient over `(n k)` - wedderburn_etherington_number/1 - Count of permutations of binary rooted trees of size `n` - functions for calculating positions in euler/pascal/element triangles - eulerian_number/2 - euler_number - combinatorics counting methods - ... ### New Sequences - OEIS Core - A000001 - Number of groups of order n - A000002 - Kolakoski sequence - A000004 - The zero sequence - A000007 - The characteristic function of {0}: a(n) = 0^n - A000012 - The simplest sequence of positive numbers: the all 1's sequence - A000027 - The positive integers - A000032 - Lucas numbers beginning at 2 - A000035 - Period 2: repeat [0, 1] - A000040 - The prime numbers. - A000043 - Mersenne exponents: primes p such that 2^p - 1 is prime. - A000069 - Odious numbers: numbers with an odd number of 1's in their binary expansion - A000081 - Number of unlabeled rooted trees with n nodes - A000085 - Number of self-inverse permutations on n letters, also known as involutions - A000105 - Number of free polyominoes (or square animals) with n cells - A000108 - Catalan numbers: C(n), Also called Segner numbers. - A000109 - Number of simplicial polyhedra with n nodes - A000110 - Bell or exponential numbers: number of ways to partition a set of n labeled elements - A000111 - Euler or up/down numbers - A000112 - Number of partially ordered sets ("posets") with n unlabeled elements - A000120 - 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n) - A000124 - Central polygonal numbers (the Lazy Caterer's sequence) - A000129 - Pell numbers: a(n) = 2*a(n-1) + a(n-2) - A000142 - Factorial numbers: n! = 1*2*3*4*...*n - A000166 - Subfactorial or rencontres numbers, or derangements of `n` - A000169 - Number of labeled rooted trees with n nodes: n^(n-1) - A000204 - Lucas numbers (beginning with 1) - A000217 - Triangular numbers: a(n) = binomial(n+1,2) - A000219 - Number of planar partitions (or plane partitions) of n - A000225 - a(n) = 2^n - 1 - A000262 - Number of "sets of lists" - A000272 - Number of trees on n labeled nodes - A000292 - Tetrahedral (or triangular pyramidal) numbers - A000312 - a(n) = n^n; number of labeled mappings from n points to themselves - A000326 - Pentagonal numbers: a(n) = n*(3*n-1)/2. - A000330 - Square pyramidal numbers - A000364 - Euler (or secant or "Zig") numbers - A000521 - Coefficients of modular function j as power series in q = e^(2 Pi i t) - A000583 - Fourth powers: a(n) = n^4. - A000594 - Ramanujan's tau function - A000609 - Number of threshold functions of n or fewer variables - A000670 - Fubini numbers - A000688 - Number of Abelian groups of order n - A000720 - pi(n), the number of primes <= n. - A000796 - Decimal expansion of Pi - A000798 - Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements - A001190 - Wedderburn-Etherington numbers: unlabeled binary rooted trees - A001227 - Number of odd divisors of n. - A001477 - The nonnegative integers. - A001511 - The ruler function: 2^a(n) divides 2n - A002106 - Number of transitive permutation groups of degree n - A002654 - Number of ways of writing n as a sum of at most two nonzero squares, where order matters - A003094 - Number of unlabeled connected planar simple graphs with n nodes - A003484 - Radon function, also called Hurwitz-Radon numbers - A005470 - Number of unlabeled planar simple graphs with n nodes - A006966 - Number of lattices on n unlabeled nodes - A008292 - Triangle of Eulerian numbers T(n,k) - A055512 - Lattices with n labeled elements - OEIS Factors - A001826 - Number of divisors of n of form 4k+1 - A001842 - Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)) ## v0.10.0 ``` OEIS Coverage 144 total sequences By Module Elixir.Chunky.Sequence.OEIS - 3 sequences Elixir.Chunky.Sequence.OEIS.Core - 24 sequences Elixir.Chunky.Sequence.OEIS.Factors - 96 sequences Elixir.Chunky.Sequence.OEIS.Primes - 1 sequences Elixir.Chunky.Sequence.OEIS.Sigma - 20 sequences Sequence Groups OEIS Core Sequences - 25 / 177 (14.12%) ``` ### Enhancements - Chunky.Math - jordan_totient/2 - Jordan totient `J-k(n)` - mobius_function/1 - Classical mobius function - omega/1 - Count of distinct prime factors - bigomega/1 - Count of distinct prime factors, with multiplicity - greatest_prime_factor/1 - largest prime factor of `n` - least_prime_factor/1 - smallest prime factor of `n` - tau/1 - Tau function, number of divisors of `n` - is_squarefree?/1 - Are any factors of `n` perfect squares? - is_cubefree?/1 - Are any factors of `n` perfect cubes? - radical/1 - Square-free kernel, or `rad(n)` - product of distict prime factors - prime_factor_exponents/1 - Find the exponents of all prime factors of `n` - is_power_of?/2 - Is `n` a power of `m`? - is_sphenic_number?/1 - Is `n` the product of three distinct primes? ### New Sequences - A007434 - Jordan-2 totient `J_2(n)` - A059376 - Jordan function J_3(n) - A059377 - Jordan function J_4(n) - A059378 - Jordan function J_5(n) - A065958 - a(n) = n^2*Product_{distinct primes p dividing n} (1+1/p^2) - A065959 - a(n) = n^3*Product_{distinct primes p dividing n} (1+1/p^3) - A065960 - a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4) - A069091 - Jordan function J_6(n) - A069092 - Jordan function J_7(n) - A069093 - Jordan function J_8(n) - A069094 - Jordan function J_9(n) - A069095 - Jordan function J_10(n) - A160889 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4 - A160891 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5 - A160893 - a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n) - A160895 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7 - A160897 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8 - A160908 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9 - A160953 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10 - A160957 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11 - A160960 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 12 - A001615 - Dedekind psi function - A008683 - Möbius (or Moebius) function mu(n) - A001221 - Number of distinct primes dividing n (also called omega(n)) - A001222 - Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)) - A006530 - Gpf(n): greatest prime dividing n - A020639 - Lpf(n): least prime dividing n - A000244 - Powers of 3 - A000290 - The squares: a(n) = n^2 - A000302 - Powers of 4: a(n) = 4^n - A000578 - The cubes: a(n) = n^3. - A001358 - Semiprimes (or biprimes): products of two primes - A005117 - Squarefree numbers: numbers that are not divisible by a square greater than 1 - A000037 - Numbers that are not squares - A000977 - Numbers that are divisible by at least three different primes - A004709 - Cubefree numbers: numbers that are not divisible by any cube > 1 - A006881 - Squarefree semiprimes: Numbers that are the product of two distinct primes - A007018 - a(n) = a(n-1)^2 + a(n-1), a(0)=1 - A007304 - Sphenic numbers: products of 3 distinct primes - A007412 - The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ] - A007774 - Numbers that are divisible by exactly 2 different primes - A007947 - Largest squarefree number dividing n - A008966 - 1 if n is squarefree, else 0. - A013929 - Numbers that are not squarefree. - A014612 - Numbers that are the product of exactly three primes, including multiplicity. - A014613 - Numbers that are products of 4 primes - A014614 - Numbers that are products of 5 primes - A030513 - Numbers with 4 divisors - A030515 - Numbers with exactly 6 divisors - A033273 - Number of nonprime divisors of n - A033942 - At least 3 prime factors (counted with multiplicity). - A033987 - Numbers that are divisible by at least 4 primes (counted with multiplicity) - A033992 - Numbers that are divisible by exactly three different primes - A033993 - Numbers that are divisible by exactly four different primes - A036537 - Numbers whose number of divisors is a power of 2. - A037143 - Numbers with at most 2 prime factors (counted with multiplicity). - A038109 - Divisible exactly by the square of a prime. - A039956 - Even squarefree numbers. - A046099 - Numbers that are not cubefree. Numbers divisible by a cube greater than 1. - A046306 - Numbers that are divisible by exactly 6 primes with multiplicity. - A046308 - Numbers that are divisible by exactly 7 primes counting multiplicity. - A046310 - Numbers that are divisible by exactly 8 primes counting multiplicity - A046312 - Numbers that are divisible by exactly 9 primes with multiplicity - A046314 - Numbers that are divisible by exactly 10 primes with multiplicity - A046321 - Odd numbers divisible by exactly 8 primes (counted with multiplicity) - A046386 - Products of four distinct primes - A046387 - Products of 5 distinct primes - A046660 - Excess of n = Ω(n) - ω(n) - A048272 - Number of odd divisors of n minus number of even divisors of n - A051270 - Numbers that are divisible by exactly 5 different primes - A056911 - Odd squarefree numbers. - A059269 - Numbers n for which tau(n) is divisible by 3. - A067259 - Cubefree numbers which are not squarefree - A067885 - Product of 6 distinct primes - A069272 - 11-almost primes (generalization of semiprimes) - A069273 - 12-almost primes (generalization of semiprimes) - A069274 - 13-almost primes (generalization of semiprimes) - A069275 - 14-almost primes (generalization of semiprimes) - A069276 - 15-almost primes (generalization of semiprimes) - A069277 - 16-almost primes (generalization of semiprimes) - A069278 - 17-almost primes (generalization of semiprimes) - A069279 - Products of exactly 18 primes (generalization of semiprimes) - A069280 - 19-almost primes (generalization of semiprimes) - A069281 - 20-almost primes (generalization of semiprimes) - A074969 - Numbers with six distinct prime divisors - A076479 - a(n) = mu(rad(n)), where mu is the Moebius-function - A117805 - Start with 3. Square the previous term and subtract it. - A123321 - Products of 7 distinct primes - A123322 - Products of 8 distinct primes - A130897 - Numbers that are not exponentially squarefree. - A162643 - Numbers such that their number of divisors is not a power of 2. - A209061 - Exponentially squarefree numbers - A211337 - Numbers n for which the number of divisors, tau(n), is congruent to 1 modulo 3 - A211338 - Numbers n for which the number of divisors, tau(n), is congruent to 2 modulo 3 ## v0.9.0 ### Changes/Refactorizations ### Enhancements - Chunky.Math - is_abundant?/1 - Is a number `n` an Abundant number - next_abundant/1 - Find the next abundant number after `n` - is_perfect?/1 - Is a number `n` a perfect number - is_deficient?/1 - Is a number `n` a deficient number - next_deficient/1 - Find the next deficient number - is_arithmetic_number?/1 - Is a number `n` an arithmetic number - aliquot_sum/1 - Aliquot Sum of `n` - is_highly_abundant?/1` - Is a number `n` highly abundant? - is_powerful_number?/1 - Is a number `n` a powerful number? - product_of_prime_factors/1 - Number theoretical function for product of prime factor exponents of `n` - is_highly_powerful_number?/1 - Is a number a _highly powerful_ number? - is_perfect_power?/1 - Is integer `n` a perfect power? - is_perfect_square?/1 - Is integer `n` a perfect square? - is_perfect_cube?/1 - Is integer `n` a perfect cube? - is_root_of?/2 - Is integer `n` any k-th root of `m`? - is_achilles_number?/1 - Is integer `n` an achilles number? - is_coprime?/2 - Test if `m` and `n` are co-prime - totient/1 - Calculate Euler's totient for `n` - Chunky.Sequence - drop/2 - Like Enum.drop ### New Sequences - A001065 - Aliquot parts of N - A005101 - Abundant Numbers - A000396 - Perfect Numbers - A005100 - Deficient Numbers - A003601 - Arithmetic Numbers - A002093 - Highly Abundant Numbers - Added Sequences.OEIS.Factors module - A001694 - Powerful Numbers - A005361 - Product of Prime Exponents of factors of N - A005934 - Highly powerful numbers: numbers with record value - A001597 - Perfect Powers - A052486 - Achilles Numbers - A000010 - Euler's totient function ## v0.8.0 ### Changes/Refactorizations ### Enhancements - Chunky.Sequence - sequences are now marked as finite or infinite (as computable/stored in Squence library) - sequences can now have initial index/offset other than 0 (like A000593) - New Functions: - `is_finite?/1` - Is a sequence finite or infinite is sequence library? - Chunky.Math - `factors/1` - All divisors of N - `sigma/1` - Sigma-1 function of factors of N - `sigma/2` - Generalized Sigma function - `pow/2` - Pure integer exponentiation ### New Sequences - A000593 - Sum of Odd Divisors of N - A000009 - Number of partitions of n into distinct parts - A000079 - Powers of 2 - A000203 - Sigma-1 of N - A001057 through A001060 - sigma2 through sigma5 of N - A013954 through A013968 - sigma6 through sigma20 of N ## v0.7.0 ### Enhancements - `Chunky.Math` - Extended math for integers and floating point - `pow/3` - Modular arithmetic exponentiation - `is_prime?/1` - Primality test for integers - `prime_factors/1` - Factorize an integer to prime factors - `Chunky.Sequences` - Create, inspect, manipulate, iterate, and compare finite and infinite value sequences - New functions: - `create/3` - Create a new sequence instance - `available/0` - List all loaded sequences from all loaded applications and modules - `available/1` - List available sequences from a module - `has_next?/1` - Check that a sequence has at least one more available value - `is_available?/2` - Check if a specific sequence is available - `is_instance/2` - Check if a sequence is an instance of a specific sequence identifier - `is_instance/3` - Check if a sequence is an instance of a specific sequence identifier - `get_references/1` - Retrieve reference sources and links for a sequence - `has_reference?/2 - Check if a sequence has a specific reference source - `readable_name/1` - Find the human readable name of a sequence - `next/1` - Retrieve the next sequence value and updated sequence struct as a tuple - `next!/1` - Retrieve the next sequence as just an updated sequence struct - `take/2` - Like `Enum.take/2` - retrieve a list of values from a sequence - `take!/2` - Like `take/2`, but only return the updated sequence struct - `sequence_for_function/1` - Wrap a function as a sequence - see Developing New Sequences - `sequence_for_list/1` - Wrap a list as a sequence - see Developing New Sequences - `map/2` - Apply a function to values in a sequence, and collect the result - New Sequences: - `{Basic, :whole_numbers}` - Whole number sequence, starting from `1` or any other digit - `{Basic, :empty}` - The empty sequence - `{Basic, :decimal_digits}` - The decimal digits - `{OEIS, :a000045}` - OEIS - Fibonacci sequence - `{OEIS, :fibonacci}` - OEIS - alternate name, Fibonacci sequence - `{OEIS, :keyword_core}` - OEIS - List of core sequences, according to OEIS - `{OEIS, :a000041}` - OEIS - Partitions of Integers - Various test sequences ## v0.6.5 ### Enhancements - `Chunky.Fractions` - added `uniq/2` for finding distinct fractions in a list - added `sort/2` for sorting value lists - added `clamp/2` for constraining value lists ## v0.6.4 ### Enhancements - `Chunky.Fraction` - Most functions now use type coercion to handle any value that can be converted to a fraction via `new/1` ## v0.6.3 ### Enhancements - `Chunky.Fraction` - `to_float/2` - convert to a float, with optional precision rounding - `min_of/1` - find the smallest from a list of fractions - `min_of/2` - find the smallest of two fractions - `Chunky.Grid` - `put_all/2` - basic function for putting `{x, y, v}` tuples or `%{x: x, y: y, value: value}` maps into the grid - `find_index/2` - Find coordinates in grid of a value ## v0.6.2 ### Documentation - `Chunky.Fraction` - Enhancements to documentation. Extended doctests ## v0.6.1 ### Enhancements - `Chunky.Grid` - `put_at/3` and `put_at/4` - put values into the grid ## v0.6.0 ### Enhancements - `Chunky.Fraction` module for manipulating fractions - `new/2` - create a new fraction - `new/1` - create a new fraction from a tuple or integer - `has_whole?/1` - fractions is greater than 1, and has a whole component - `is_whole?/1` - does a fraction exactly represent a whole number - `components/1` - tuple of numerator an denominator - `get_whole/1` - get reduced whole component of a fraction - `get_remainder/1` - get remainder of fraction after removing whole components - `split/1` - combine `get_whole/1` and `get_remainder/1` into one call - `is_simplified?/1` - is fraction in reduced form? - `simplify/1` - reduce fraction - `is_zero?/1` - does fraction represent zero? - `add/3` - Add two fractions, or a fraction and an integer - `subtract/3` - Subtract two fractions, or a fraction and an integer - `String.Chars` - Fractions now work properly with IO functions - `multiply/3` - Multiply two fractions, or a fraction and an integer - `reciprocal/2` - Take the reciprocal of a fraction - `divide/3` - Divide two fractions, or a fraction and an integer - `normalize/2` - Normalize two fractions to a common denominator - `is_positive?/1` - Test if a fraction is positive - `is_negative?/2` - Test if a fraction is negative - `power/3` - Fractional and integer powers of integers and fractions - `gt?/2`, `gte?/2`, `lt?/2`, `lte?/2`, and `eq?/2` added for comparison between fractions and fractions and integers - `normalize_all/1` - normalize a list of fractions and integers, like `normalize/2` - `sum/2` - sum a list of fractions and integers - `lcm/1` - find Least Common Multiple from a list of integers - `Chunky.Grid` module for working with two dimensional data - `Grid.new/3` - generate a grid from a value or a function - `Grid.get_at/2` and `Grid.get_at/3` - access cell value by 2d index - `Grid.valid_coordinate/*` and `Grid.valid_coordinate?/*` - determine if a coordinate is within grid bounds ## v0.5.0 ### Enhancements - `Chunky.combinations_size/2` - pre-calculate the size of a combination using a closed form equation, instead of running the combination ## v0.4.1 ### Documentation - Fixes for embedded `@moduledoc` for better Hexdocs layout ## v0.4.0 ### Enhancements - `Chunky.permutations_size/1` - pre-calculate the size of a permutation using a closed form equation, instead of running the permutation ## v0.3.0 ### Enhancements - Added `Chunky.combinations/2` for nCr unordered set generation ### Documentation - move all TODO items out of Chunky module - remove references to incomplete/unimplemented functions ## v0.2.1 ### Documentation - Fix reference to `Chunky.chunk_length/2` in moduledoc ## v0.2.0 ### Enhancements - `Chunky.chunk_length/2` added. Supports `list`, `tuple`, `binary`, and `range` types ### Documentation - Cleanup of readme and top level documentation - Hexdocs now have embedded readme data ## v0.1.1 ### Documentation - Expanded documentation for `Chunky.permutations/1` ## v0.1.0 ### Enhancements - `Chunky.permutations/1` added. Supports `list`, `tuple`, `binary`, and `range` types