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extendSequence :: SequenceData -> SequenceDataoeis Math.OEIS 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 xs. If the matched OEIS sequence contains any elements prior to those matching xs, they will be dropped. In addition, if no matching sequences are found, xs will be returned unchanged. The result is not in the IO 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 getSequenceByID changing, but still unlikely enough to be essentially a non-issue. Again, purists may use extendSequence_IO). Examples:
Prelude 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...
Prelude Math.OEIS> extendSequence [2,4,8,16,32] [2,4,8,16,32,64,128,256,512,1024,2048,4096,8192...
Prelude Math.OEIS> extendSequence [9,8,7,41,562] -- nothing matches [9,8,7,41,562]
extendSequence_IO :: [Integer] -> IO [Integer]oeis Math.OEIS The same as extendSequence, but in the IO monad.
getSequenceByID :: String -> Maybe SequenceDataoeis Math.OEIS 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 Handbook of Integer Sequences/) can be used as well. Note that the result is not in the IO 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:
Prelude 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! Nothing
getSequenceByID_IO :: String -> IO (Maybe SequenceData)oeis Math.OEIS The same as getSequenceByID, but with a result in the IO monad.
lookupSequence :: SequenceData -> Maybe OEISSequenceoeis Math.OEIS 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 IO monad applies.
lookupSequenceByID :: String -> Maybe OEISSequenceoeis Math.OEIS 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 IO 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]
lookupSequenceByID_IO :: String -> IO (Maybe OEISSequence)oeis Math.OEIS The same as lookupSequenceByID, but in the IO monad.
lookupSequence_IO :: SequenceData -> IO (Maybe OEISSequence)oeis Math.OEIS The same as lookupSequence, but in the IO monad.
lookupSequences_IO :: SequenceData -> IO [OEISSequence]oeis Math.OEIS Similar to lookupSequence_IO, but return up to 10 results.
searchSequence_IO :: String -> IO (Maybe OEISSequence)oeis Math.OEIS Look up a sequence in the OEIS using its search function.