Module: sage.databases.sloane
Interface to Sloane On-Line Encyclopedia of Integer Sequences
TODO:
- When this program gets a sloane sequence from the database it actually downloads a huge amount of information about it, then throws most of it away. Also, it returns the data to the user as a very simple tuple. It would be much better to return an instance of a class
class SloaneSequence: ...
and the class should have methods for each of the things that Sloane records about a sequence. Also, when possible, it should be able to compute more terms.
To look up sequence A060843, type one of the following:
sage: sloane_sequence(60843) # optional -- requires internet Searching Sloane's online database... [60843, 'Busy Beaver problem: maximal number of steps that an n-state Turing machine can make on an initially blank tape before eventually halting.', [1, 6, 21, 107]]
sage: sloane_sequence("60843") # optional -- requires internet Searching Sloane's online database... [60843, 'Busy Beaver problem: maximal number of steps that an n-state Turing machine can make on an initially blank tape before eventually halting.', [1, 6, 21, 107]]
sage: sloane_sequence("060843") # optional -- requires internet Searching Sloane's online database... [60843, 'Busy Beaver problem: maximal number of steps that an n-state Turing machine can make on an initially blank tape before eventually halting.', [1, 6, 21, 107]]
Do not prefix an integer with a 0 or it will be interpreted in octal.
Results are of the form [number, description, list], and invalid
numbers will cause sloane_sequence
to raise an ValueError exception:
sage: sloane_sequence('sage') # optional -- requires internet Traceback (most recent call last): ... ValueError: sequence 'sage' not found
To look up the sequence
sage: sloane_find([2,3,5,7], 2) # optional -- requires internet Searching Sloane's online database... [[40, 'The prime numbers.', [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271]], [41, 'a(n) = number of partitions of n (the partition numbers).', [1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134]]]
To return no more than 2 results (default is 30), type
sage: sloane_find([1,2,3,4,5], 2) # optional -- requires internet Searching Sloane's online database... [[27, 'The natural numbers. Also called the whole numbers, the counting numbers or the positive integers.', [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77]], [961, 'Prime powers.', [1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227]]]
Note that the OEIS (http://www.research.att.com/ njas/sequences/) claims to limit the number of results to 100. Results are lists of the form [ [number, description, list]], and invalid input will cause sloane_find to return [].
In some cases, these functions may return [] even though the inputs are legal. These cases correspond to errors from the OEIS server, and calling the functions again may fix the problem.
Alternatively, the SloaneEncyclopedia object provides access to a local copy
of the database containing only the sequences. To use this you must install
the optional database_sloane_oeis-2005-12 package using
sage -i database_sloane_oeis-2005-12
.
To look up a sequence, type
sage: SloaneEncyclopedia[60843] [1, 6, 21, 107]
To search locally for a particular subsequence, type
sage: SloaneEncyclopedia.find([1,2,3,4,5], 1) [(15, [1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, 13, 13, 16, 16, 16, 17, 19, 19, 23, 23, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 32, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 49, 49, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 64, 64, 64, 67, 67, 67, 71, 71, 71, 71, 73])]
The default maximum number of results is 30, but to return up to 100, type
sage: SloaneEncyclopedia.find([1,2,3,4,5], 100) [(15, [1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, ...
Results in either case are of the form [ (number, list) ].
Author Log:
Module-level Functions
text) |
list, [nresults=30], [verbose=True]) |
number) |
Class: SloaneEncyclopediaClass
self) |
Initialize the database but do not load any of the data.
Functions: find,
load,
unload
self, seq, [maxresults=30]) |
Return a list of all sequences which have seq as a subsequence, up to maxresults results. Sequences are returned in the form (number, list).
Input:
self) |
Load the entire encyclopedia into memory from a file. This is done automatically if the user tries to perform a lookup or a search.
self) |
Remove the database from memory.
Special Functions: __getitem__,
__init__,
__iter__,
__len__,
__repr__
self, N) |
Return sequence N in the encyclopedia. If sequence N does not exist, return [].
Input:
self) |
Returns an iterator through the encyclopedia. Elements are of the form [number, sequence].
self) |
Return the number of sequences in the encyclopedia.
self) |
String representation of this database. Output: str
See About this document... for information on suggesting changes.