úÎRSMúS      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSafe_Data structure for storing an OEIS entry. For more information on the various components, see  http://oeis.org/eishelp2.html.,Catalog number(s), e.g. A000040, N1425. (%I)mThe actual sequence data (or absolute values of the sequence data in the case of signed sequences). (%S,T,U)OSigned sequence data (empty for sequences with all positive entries). (%V,W,X)'Short description of the sequence. (%N)!List of academic references. (%D)2List of links to more information on the web. (%H)2Formulas or equations involving the sequence. (%F) )Cross-references to other sequences. (%Y) 5Author who input the sequence into the database. (%A) 'Subscript/index of the first term. (%O) "Index of the first term > 1. (%O) 8Code that can be used to generate the sequence. (%p,t,o)'Corrections, extensions, or edits. (%E)Examples. (%e)Keywords. (%K)Comments. (%C)IOEIS keywords. For more information on the meaning of each keyword, see  http://oeis.org/eishelp2.html#RK./ÿ Programming language that some code to generate the sequence is written in. The only languages indicated natively by the OEIS database are Mathematica and Maple; any other languages will be listed (usually in parentheses) at the beginning of the actual code snippet.4  !"#$%&'()*+,-./01234  !"#$%&'()*+,-./0123  !"#$%&'()*+,-./0123None456789:;<=>?@ABCDEFGH456789:;<=>?@ABCDEFGH456789:;<=>?@ABCDEFGH456789:;<=>?@ABCDEFGHNone IHInterpret a string as a OEIS request, and return the results as Strings.J9Look up a sequence in the OEIS using its search function.K˜Look up a sequence in the OEIS by its catalog number. Generally this would be its A-number, but M-numbers (from the /Encyclopedia of Integer Sequences) and N-numbers (from the 5Handbook of Integer Sequences/) can be used as well.#Note that the result is not in the Sÿ monad, even though the implementation requires looking up information via the Internet. There are no side effects to speak of, and from a practical point of view the function is referentially transparent (OEIS A-numbers could change in theory, but it's extremely unlikely). Examples: ÄPrelude Math.OEIS> getSequenceByID "A000040" -- the prime numbers Just [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47... Prelude Math.OEIS> getSequenceByID "nosuch" -- no such sequence! NothingL The same as K, but with a result in the S monad.M…Look up a sequence by ID number, returning a data structure containing the entirety of the information the OEIS has on the sequence./The standard disclaimer about not being in the S monad applies. Examples: ¸Prelude Math.OEIS> description `fmap` lookupSequenceByID "A000040" Just "The prime numbers." Prelude Math.OEIS> keywords `fmap` lookupSequenceByID "A000105" Just [Nonn,Hard,Nice,Core]N The same as M , but in the S monad.O—Extend a sequence by using it as a lookup to the OEIS, taking the first sequence returned as a result, and using it to augment the original sequence. Note that xs! is guaranteed to be a prefix of extendSequence xsN. If the matched OEIS sequence contains any elements prior to those matching xsJ, they will be dropped. In addition, if no matching sequences are found, xs will be returned unchanged.The result is not in the SÿB monad even though the implementation requires looking up information via the Internet. There are no side effects, and practically speaking this function is referentially transparent (technically, results may change from time to time when the OEIS database is updated; this is slightly more likely than the results of K] changing, but still unlikely enough to be essentially a non-issue. Again, purists may use P). Examples: hPrelude Math.OEIS> extendSequence [5,7,11,13,17] [5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71... bPrelude Math.OEIS> extendSequence [2,4,8,16,32] [2,4,8,16,32,64,128,256,512,1024,2048,4096,8192... TPrelude Math.OEIS> extendSequence [9,8,7,41,562] -- nothing matches [9,8,7,41,562]P The same as O , but in the S monad.T extend xs ext returns the maximal suffix of ext of which xs is a prefix, or xs if xs$ is not a prefix of any suffixes of ext. It is guaranteed that .forall xs ext. xs `isPrefixOf` (extend xs ext)Q“Find a matching sequence in the OEIS database, returning a data structure containing the entirety of the information the OEIS has on the sequence./The standard disclaimer about not being in the S monad applies.R The same as Q , but in the S monad. IJKLMNOPTQR>  !"#$%&'()*+,-./0123IJKLMNOPQR>KMOQLNPRJI3/012 !"#$%&'()*+,-.  IJKLMNOPTQRU      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[5Ti4rfi1iTO2FO0Ch7daQf Math.OEISMath.OEIS.InternalMath.OEIS.Types OEISSequenceOEIS catalogNums sequenceData signedData description referenceslinksformulasxrefsauthoroffsetfirstGT1programs extensionsexampleskeywordscommentsKeywordBaseBrefChangedCofrConsCoreDeadDumbDupeEasyEigenFiniFracFullHardMoreMultNewNiceNonnObscSignTabfTablUnedUnknWalkWordLanguage MathematicaMapleOther SequenceData baseSearchURI idSearchURI seqSearchURIgetOEISgetrequest readKeyword capitalize emptyOEIS addElement parseOEIS parseRawOEIS parseKeywordscsvItemsdel parseItem combineConts splitWordisItem joinContstrimLeft lookupOEISsearchSequence_IOgetSequenceByIDgetSequenceByID_IOlookupSequenceByIDlookupSequenceByID_IOextendSequenceextendSequence_IOlookupSequencelookupSequence_IOghc-prim GHC.TypesIOextend