defmodule OEIS do @moduledoc """ A client for the On-Line Encyclopedia of Integer Sequences (OEIS). """ alias OEIS.Sequence @base_url "https://oeis.org" @max_sequence_terms 6 @string_fields [ :keyword, :comment, :ref, :link, :formula, :example, :name, :xref, :subseq ] @doc """ Searches the OEIS database. This function is the main entry point for querying the OEIS. It can be called with a keyword list of search parameters, a raw list of integers (treated as a sequence), or a raw string. When called with a string, it will be treated as an OEIS ID if it matches the `A` number format (e.g., `"A000055"`), otherwise it will be treated as a comma-separated or space-separated sequence (e.g., `"1,2,3,4"` or `"1 2 3 4"`). An optional keyword list of options can be provided as the second argument. Supported options: * `:may_truncate` (boolean): If `true` (default), long sequences (more than 6 terms) will be truncated and leading 0s/1s removed to improve search results. If `false`, the sequence is searched exactly as provided. * `:respect_sign` (boolean): If `true` (default), the search will respect the signs of the numbers in the sequence (using the `signed:` prefix). If `false`, the search will ignore signs (using the `seq:` prefix). On success, returns `{:single, sequence}` for an exact ID match, or `{:multi, list_of_sequences}` for other searches. `list_of_sequences` is a list of `OEIS.Sequence` structs. If no results are found, `{:no_match, "No matches found."}` is returned. If a query returns a full page of results (currently 10 sequences for general searches), it implies there might be more results available. In such cases, a `{:partial, list_of_sequences}` tuple is returned. ## Search Hints * **Term Limit:** Providing too many terms can often lead to no results because the sequence in the database might be shorter or differ slightly. This function automatically truncates long sequences to 6 terms (excluding leading 0s and 1s) to improve match rates. * **Leading Terms:** It is often helpful to omit the first few terms if the sequence has many leading 0s or 1s, or if the starting value is conventional (e.g. starting at n=0 vs n=1). * **Gaps:** If your sequence has many zeros (e.g., `1, 0, 2, 0, 4, 0`), try removing the zeros (`1, 2, 4`) for a better search. * **Formats:** Sequences can be supplied as lists of integers, comma-separated strings, or space-separated strings. ## Parameters When called with a keyword list, the following keys are accepted: * `:sequence` (list of integers, or a string): A list of terms in the sequence to search for. If the sequence has more than 6 terms, it will be automatically adjusted: leading 0s and 1s will be removed, and if it remains longer than 6 terms, it will be truncated to the first 6 terms. * Example: `[1, 2, 3, 6, 11, 23]`, `"1,2,3,6,11,23"`, or `"1 2 3 6 11 23"` * `:id` (string): An OEIS A-number to search for. * Example: `"A000055"` * `:keyword` (string): A keyword to filter results. * Example: `"core"` * `:author` (string): An author's name to filter results. The search is automatically made greedy by surrounding the name with `*`. * Example: `"Sloane"` * `:query` (string): A general query string for other search terms. * Example: `"number of partitions"` * `:start` (integer): The starting index for results, used for pagination. * Default is 0. ## Examples iex> OEIS.search("A000045") {:single, %OEIS.Sequence{id: "A000045", name: "Fibonacci numbers." <> _}} iex> OEIS.search([1, 2, 3, 5, 8]) {:multi, [%OEIS.Sequence{id: "A000045", name: "Fibonacci numbers." <> _}]} iex> OEIS.search(query: "non-existent query") {:no_match, "No matches found."} iex> OEIS.search(author: "Sloane", keyword: "core", start: 10) {:partial, list_of_sequences} iex> {:partial, sequences} = OEIS.search(sequence: [1, 2, 3]) iex> length(sequences) 10 # A broad query like "prime number" often returns no results from the JSON API, # which now translates to `{:no_match, "No matches found."}`. The OEIS JSON API # currently does not provide a distinct indicator for "too many results" # versus "no results" in its JSON response. iex> OEIS.search(query: "prime number") {:no_match, "No matches found."} """ def search(query, options \\ []) def search(num, options) when is_integer(num) do do_search([id: "A" <> String.pad_leading(to_string(num), 6, "0")], options) end def search(str, options) when is_binary(str) do handle_string_search(str, options) end def search(list, options) when is_list(list) do case Keyword.keyword?(list) do true -> do_search(list, options) false -> do_search([sequence: list], options) end end def search(_other, _options) do {:error, {:bad_param, "Input must be a keyword list, a list of integers, or a string."}} end @default_options [ may_truncate: true, respect_sign: true, max_concurrency: 5, timeout: 15_000 ] defp ensure_options(opts) do Keyword.merge(@default_options, opts) end @doc """ Fetches more terms for an OEIS sequence from its associated "b-file". This function takes an `OEIS.Sequence` struct, identifies the single link pointing to an `oeis.org/.../b.txt` file (which contains the extra data), fetches its content, and extracts the integer values from the second column of each line. The leading index column in these `.txt` files is ignored. The fetched terms replace the existing ones in the sequence. Returns `{:ok, updated_sequence}` on success, where `updated_sequence` is the original sequence with its `data` field updated with the new terms. Returns `{:error, %{original_sequence: original, message: error_message}}` on failure, including cases where no extra data link is found, no integer data can be extracted, or an HTTP request/parsing error occurs. ## Parameters * `sequence` (OEIS.Sequence): The OEIS sequence struct containing links. ## Examples iex> OEIS.search("A000001") ...> |> case do ...> {:single, seq} -> OEIS.fetch_more_terms(seq) ...> _ -> {:error, %{message: "Sequence not found"}} ...> end {:ok, %OEIS.Sequence{id: "A000001", data: [0, 1, 1, 2, 1, 2, 2, 1, 5, 2, 2, ...]}} # Example shortened """ def fetch_more_terms(sequence, options \\ []) def fetch_more_terms(%OEIS.Sequence{} = original_sequence, options) do opts = ensure_options(options) case Enum.find(original_sequence.link, &Map.get(&1, :extra_data, false)) do nil -> {:error, %{ original_sequence: original_sequence, message: "No extra data link found for this sequence." }} %{url: url, text: title} = link -> case process_b_file_link(link, url, title, opts) do {:extra_data, data} -> {:ok, %{original_sequence | data: data}} {:no_match, message} -> {:error, %{original_sequence: original_sequence, message: message}} {:error, reason} -> {:error, %{original_sequence: original_sequence, message: reason}} end end end def fetch_more_terms(_other, _options) do {:error, %{message: "Input must be an OEIS.Sequence struct."}} end @doc """ Fetches the sequence definitions for the IDs listed in the sequence's `xref` field. This function extracts OEIS IDs (e.g., "A000045") from the cross-reference strings and performs parallel searches for each ID found. It uses `Task.async_stream/4` to fetch them concurrently. ## Options * `:max_concurrency` - The maximum number of concurrent requests (default: 5). * `:timeout` - The timeout for each request in milliseconds (default: 15_000). ## Examples iex> {:single, seq} = OEIS.search("A000045") iex> related_sequences = OEIS.fetch_xrefs(seq, max_concurrency: 3) iex> Enum.map(related_sequences, & &1.id) ["A000032", "A001622", ...] # List of related IDs """ def fetch_xrefs(sequence, options \\ []) def fetch_xrefs(%OEIS.Sequence{xref: xref}, options) do opts = ensure_options(options) max_concurrency = opts[:max_concurrency] timeout = opts[:timeout] xref |> extract_xref_ids() |> Task.async_stream( fn id -> case search(id) do {:single, seq} -> seq _ -> nil end end, max_concurrency: max_concurrency, timeout: timeout ) |> Enum.map(fn {:ok, result} -> result _ -> nil end) |> Enum.reject(&is_nil/1) end def fetch_xrefs(_other, _options) do {:error, %{message: "Input must be an OEIS.Sequence struct."}} end defp process_b_file_link(%{url: url, text: title}, _url, _title, opts) do case fetch_and_parse_extra_data(url, opts) do {:ok, data} -> case data do [] -> {:no_match, "No integer data extracted from extra data for link: #{title}"} # <--- Modified _ -> {:extra_data, data} end {:error, reason} -> {:error, reason} end end defp fetch_and_parse_extra_data(url, opts) do req_opts = [receive_timeout: opts[:timeout]] case Req.get(url, req_opts) do {:ok, %{status: 200, body: body}} -> parse_extra_data_content(body) {:ok, %{status: status, body: body}} -> {:error, {:http_error, "Failed to fetch extra data from #{url}: HTTP #{status} - #{inspect(body)}"}} {:error, reason} -> {:error, {:http_error, "Failed to fetch extra data from #{url}: #{inspect(reason)}"}} end end defp parse_extra_data_content(content) when is_binary(content) do lines = String.split(content, ~r/\r?\n/, trim: true) extracted_integers = Enum.flat_map(lines, &parse_extra_data_line/1) {:ok, extracted_integers} end defp parse_extra_data_line(line) do case String.split(line, ~r/\s+/, trim: true) do [_, second_col_str | _] -> case Integer.parse(second_col_str) do {integer, ""} -> [integer] # Not a valid integer, ignore _ -> [] end # Line doesn't have at least two columns, ignore _ -> [] end end defp handle_string_search(<<"A", _id_num::binary-size(6)>> = a_number, options) do do_search([id: a_number], options) end defp handle_string_search(str, options) do case Integer.parse(str) do {num, ""} -> do_search([id: "A" <> String.pad_leading(to_string(num), 6, "0")], options) # Not an integer, treat as sequence _ -> do_search([sequence: str], options) end end defp do_search(terms, options) do opts = ensure_options(options) case Keyword.fetch(terms, :id) do {:ok, id} -> case make_id_request(id, opts) do {:ok, decoded_json_body} -> handle_oeis_response(decoded_json_body) err -> err end # This is the general search branch :error -> with {:ok, query_params} <- build_query_string(terms, opts), search_url = Path.join(@base_url, "/search"), {:ok, decoded_json_body} <- make_request(search_url, query_params, opts) do handle_oeis_response(decoded_json_body) else {:error, reason} -> {:error, reason} end end end defp make_id_request(id, opts) do url = Path.join(@base_url, id) make_request(url, [fmt: "json"], opts) end defp build_query_string(terms, opts) do with {:ok, query_map} <- build_base_query_map(terms, opts) do start_param = Keyword.get(opts, :start) || Keyword.get(terms, :start) handle_start_param(query_map, start_param) end end defp build_base_query_map(terms, opts) do do_build_query_terms(terms, opts, {:ok, []}) end defp do_build_query_terms([], _opts, {:ok, acc_terms}) do case Enum.empty?(acc_terms) do true -> {:error, {:bad_param, "At least one of :sequence, :id, :keyword, :author, or :query must be provided."}} false -> q_value = Enum.join(acc_terms, " ") {:ok, %{q: q_value, fmt: "json"}} end end defp do_build_query_terms([{_key, nil} | tail], opts, acc_status), do: do_build_query_terms(tail, opts, acc_status) defp do_build_query_terms([head | tail], opts, {:ok, acc_terms}) do {key, value} = head case key do :start -> do_build_query_terms(tail, opts, {:ok, acc_terms}) _ -> case add_query_term(acc_terms, opts, key, value) do {:ok, new_acc_terms} -> do_build_query_terms(tail, opts, {:ok, new_acc_terms}) {:error, _} = err -> err end end end defp do_build_query_terms(_rem, _opts, {:error, _} = err), do: err defp handle_start_param(query_map, nil), do: {:ok, query_map} defp handle_start_param(query_map, start_param) when is_integer(start_param) and start_param >= 0 do {:ok, Map.put(query_map, :start, start_param)} end defp handle_start_param(_query_map, _), do: {:error, {:bad_param, ":start must be a non-negative integer."}} defp normalize_sequence_to_list(list) when is_list(list) do case Enum.all?(list, &is_integer/1) do true -> {:ok, list} false -> {:error, "Sequence list must contain only integers."} end end defp normalize_sequence_to_list(str) when is_binary(str) do case parse_string_to_int_list(str) do {:ok, int_list} -> case int_list do [] -> {:error, "Sequence string cannot be empty."} list -> {:ok, list} end {:error, reason} -> {:error, reason} end end defp normalize_sequence_to_list(_), do: {:error, "Sequence must be a list of integers or a string of integers."} defp parse_string_to_int_list(str) do integers_and_remains = str |> String.split(~r/[\s,]+/, trim: true) |> Enum.map(&String.trim/1) |> Enum.map(&Integer.parse/1) case Enum.all?(integers_and_remains, &valid_integer_parse?/1) do true -> {:ok, Enum.map(integers_and_remains, fn {int, _rest} -> int end)} false -> {:error, "Sequence string must be a list of integers (comma or space separated)."} end end defp valid_integer_parse?({int, rest}) when is_integer(int) and rest == "", do: true defp valid_integer_parse?(_), do: false defp add_query_term(acc_terms, opts, :sequence, sequence) do case normalize_sequence_to_list(sequence) do {:ok, int_list} -> final_list = case Keyword.get(opts, :may_truncate) do true -> truncate_sequence_list(int_list) false -> int_list end prefix = case Keyword.get(opts, :respect_sign) do true -> "signed:" false -> "seq:" end {:ok, [prefix <> Enum.join(final_list, ",") | acc_terms]} {:error, reason} -> {:error, {:bad_param, reason}} end end defp add_query_term(acc_terms, _opts, :id, <<"A", _id_num::binary-size(6)>> = id) do {:ok, ["id:" <> id | acc_terms]} end defp add_query_term(_acc_terms, _opts, :id, _id), do: {:error, {:bad_param, "ID must be a string starting with 'A' and 7 characters long (e.g., 'A000001')."}} defp add_query_term(acc_terms, _opts, key, value) when key in @string_fields and is_binary(value) do {:ok, ["#{Atom.to_string(key)}:" <> value | acc_terms]} end defp add_query_term(_acc_terms, _opts, key, _value) when key in @string_fields do {:error, {:bad_param, "#{Atom.to_string(key)} must be a string."}} end defp add_query_term(acc_terms, _opts, :author, author) when is_binary(author) do {:ok, ["author:*" <> author <> "*" | acc_terms]} end defp add_query_term(_acc_terms, _opts, :author, _val), do: {:error, {:bad_param, "Author must be a string."}} defp add_query_term(acc_terms, _opts, :query, query_str) when is_binary(query_str) do {:ok, [query_str | acc_terms]} end defp add_query_term(_acc_terms, _opts, :query, _val), do: {:error, {:bad_param, "General query must be a string."}} # Catch-all for unsupported options defp add_query_term(_acc_terms, _opts, key, value), do: {:error, {:bad_param, "Unsupported option: #{inspect(key)} with value: #{inspect(value)}."}} defp truncate_sequence_list(list) do case length(list) <= @max_sequence_terms do true -> list false -> list |> Enum.drop_while(&(&1 in [0, 1])) |> case do [] -> list stripped -> stripped end |> Enum.take(@max_sequence_terms) end end defp make_request(url, query_params, opts) do req_opts = [params: query_params, receive_timeout: opts[:timeout]] case Req.get(url, req_opts) do {:ok, %Req.Response{status: 200, body: body}} -> # body is already decoded by Req (could be nil, a map, or a list) {:ok, body} {:ok, %Req.Response{status: status, body: body}} -> {:error, {:http_error, "HTTP Error: #{status} - #{inspect(body)}"}} {:error, reason} -> {:error, {:http_error, reason}} end end defp handle_oeis_response(nil), do: {:no_match, "No matches found."} # Case for when the OEIS API returns a list of results (general search). defp handle_oeis_response(results) when is_list(results) and length(results) == 10 do # Include the raw results if desired {:partial, Enum.map(results, &map_to_sequence/1)} end defp handle_oeis_response(results) when is_list(results) do case results do [] -> {:no_match, "No matches found."} _avail -> {:multi, Enum.map(results, &map_to_sequence/1)} end end # Case for when the OEIS API returns a single sequence object (map) for direct A-number lookups. defp handle_oeis_response(%{"number" => _, "data" => _} = single_result) do {:single, map_to_sequence(single_result)} end defp handle_oeis_response(other), do: {:error, {:unknown_response_format, other}} defp map_to_sequence(result) do data = Map.get(result, "data", "") {_ok, data_list} = normalize_sequence_to_list(data) created = with created_str when is_binary(created_str) <- Map.get(result, "created"), {:ok, dt, _} <- DateTime.from_iso8601(created_str) do dt else _ -> nil end time = with time_str when is_binary(time_str) <- Map.get(result, "time"), {:ok, dt, _} <- DateTime.from_iso8601(time_str) do dt else _ -> nil end %Sequence{ id: "A" <> String.pad_leading(to_string(Map.get(result, "number")), 6, "0"), number: Map.get(result, "number"), name: Map.get(result, "name"), data: data_list, comment: Map.get(result, "comment"), reference: Map.get(result, "reference"), formula: Map.get(result, "formula"), example: Map.get(result, "example"), link: extract_links_from_result(result), xref: Map.get(result, "xref"), author: extract_author(result), created: created, time: time } end defp extract_xref_ids(xrefs) do case xrefs do list when is_list(list) -> list |> Enum.flat_map(fn text -> Regex.scan(~r/A\d{6}/, to_string(text)) end) |> List.flatten() |> Enum.uniq() |> Enum.sort() _ -> [] end end defp extract_author(result) do author_regex = ~r/_([A-Za-z.\s]+?)_/ comments = Map.get(result, "comment", []) references = Map.get(result, "reference", []) all_texts = case comments do list when is_list(list) -> list _ -> [] end ++ case references do list when is_list(list) -> list _ -> [] end authors = all_texts |> Enum.flat_map(fn text -> case Regex.run(author_regex, to_string(text)) do [_whole, author] -> [String.trim(author)] _ -> [] end end) |> Enum.uniq() |> Enum.sort() case authors do [] -> nil _ -> Enum.join(authors, ", ") end end defp extract_links_from_result(result) do href_regex = ~r/href=\"([^\"]*)\">([^<]+)<\/a>/ links = Map.get(result, "link", []) Enum.flat_map(links, &parse_link_string(&1, href_regex)) end defp parse_link_string(link_str, href_regex) do case Regex.scan(href_regex, to_string(link_str)) do matches when matches != [] -> Enum.map(matches, fn [_, url, text] -> build_link_map(url, text) end) _ -> [] end end defp build_link_map(url, text) do formatted_url = format_full_url(url) link_map = %{url: formatted_url, text: text} case String.match?(formatted_url, ~r"oeis\.org/A\d+/b\d+\.txt$") do true -> Map.put(link_map, :extra_data, true) false -> link_map end end defp format_full_url("/" <> _rest = url), do: "https://oeis.org" <> url defp format_full_url(url), do: url end