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# User:Charles R Greathouse IV/Keywords

### From OeisWiki

This is a list of keywords and material relating to them: when to use and not to use, ideas for expanding them, etc. This is also a partial concordance of keyword-related messages in the Seqfan mailing list.

For an introduction to the keywords, see the official description of the keywords (terse) or clear-cut examples of keywords.

## Contents |

## New keywords

See Joerg Arndt, [1], posting to SeqFan on Apr 16 2010 (linear recurrences and [eventually] periodic sequences) and Antti Karttunen, [2], posting to SeqFan on Oct 25 2009.

## Keywords currently in use

This list is intended to be complete (and was complete as of Jan 2014).

- allocated: Sequences that have been set aside for a contributor to write a new sequence which has not yet been approved.
- allocating: Sequences are sometimes given this keyword during the allocation process. The keyword cannot be searched directly.
- base: Sequences that are most readily defined with reference to a representation in some base. I'd like to see subcategories for the base (including, perhaps, exotics such as balanced ternary, factorial base, phinary, Zeckendorf representation, Knuth's quater-imaginary base, prime base (A007924), 'hyperbinary' (A125186), Fibonacci^2 (A147561), money bases (A108536), ...). See also Alonso Del Arte, [3], posting to SeqFan on Nov 13 2009 (asking for clarification on which sequences get keyword:base) and Franklin T. Adams-Watters, [4], posting to SeqFan on Nov 12 2009.
- bref: Represents sequences with fewer than four terms displayed; see N. J. A. Sloane, Re: easy and bref, posting to SeqFan on Sep 26 2011. Compatible with most other keywords, including easy and full, see the messages preceding the above.
- changed: Introduced Jan 24 2011 for sequences which have recently been changed. See keyword:new.
- cofr: A sequence which can be interpreted as a real number with a simple continued fraction given by the terms. What offset should be used by these sequences? See Richard Mathar, [5], posting to SeqFan on Mar 31 2010. Note that convergents to continued fractions should use only keyword:frac, not keyword:cofr, since they are not actual continued fractions. Further, generalized continued fractions should not use this keyword.
- cons: A sequence which can be interpreted as a real number with a decimal expansion given by the terms. See Maximilian Hasler, format of "cons" sequences of decimal expansions, posting to SeqFan on Dec 13 2010 and OEIS format for decimal representation of constants which discuss the offset for constants in the OEIS. Also note discussion Neil Sloane, Re: Keyword:cons sequences in Maple, posting to SeqFan on Apr 09 2014 in which it is noted that programs returning the constant (rather than its decimal expansion) are acceptable for cons sequences.
- core: A core sequence of the OEIS. See keyword:nice.
- dead: A sequence which has been deleted but for which the A-number will not be re-assigned. When should be sequence be removed vs. given the dead keyword? Generally, if the sequence was added in the past few years and is redundant it should be removed. Beyond a certain age, if a sequence has remained an undetected duplicate it should merely be marked dead rather than removed.
- dumb: Little-used and largely redundant with keyword:less. In theory this is used for nonmathematical sequences but the keyword's pejorative name mostly stops it from being used that way. See User:Charles R Greathouse IV/Keywords/aesthetic.
- easy: A sequence which is easy to calculate (though perhaps not to understand). See User:Charles R Greathouse IV/Keywords/difficulty.
- eigen: A sequence invariant under some transformation. It would be nice to add metadata showing which transformations can be used. For more information, see Some canonical sequences of integers by Bernstein & Sloane.
- fini: How to handle sequences like A003504 for which a finite initial sequence is integral, but include non-integers? How to handle sequences which are conjectured to be finite? Also, for information on sub-keywords, see David Wilson, [6], posting to SeqFan on Aug 27 2009 which suggests "finite: yes, no, unknown" (other multi-valued extensions may be possible).
- frac: Should not be used for possibly-noninteger sequences until such a term is found (in which case a new sequence of denominators should be added), see Franklin T. Adams-Watters, [7], posting to SeqFan on Oct 01 2009.
- full: A finite sequence in which all terms are listed. As of 2013 this includes sequences completed in a b-file, contrary to earlier policy.
- hard: See User:Charles R Greathouse IV/Keywords/difficulty.
- hear: Introduced Jan 26, 2014 for sequences with especially nice sounds. Like keyword:nice (q.v.), this to be given sparingly. See User:Charles R Greathouse IV/Keywords/aesthetic.
- less: In many ways this is the more-polite (and broader-reaching) version of keyword:dumb. It suggests that a sequence is less-interesting, and is used especially for collections of sequences obtained by varying a parameter ("Numbers n such that n^2 divides k^n-1" for many values of k) where we have enough of the family and don't need to expand it further. It can also be used for isolated sequences. See User:Charles R Greathouse IV/Keywords/aesthetic.
- look: Introduced Jan 26, 2014 for sequences with especially nice graphs. Like keyword:nice (q.v.), this to be given sparingly. Unrelated to the earlier keyword of the same name. See User:Charles R Greathouse IV/Keywords/aesthetic.
- more: It has been suggested (Joseph S. Myers, [8], posting to SeqFan on Aug 27 2009) to move away from primarily marking sequences needing more terms in favor of automatically detecting this. It may be feasible, but I view it as a supplement rather than a replacement.
- mult: Introduced Jul 2001 for multiplicative sequences, including completely multiplicative sequences. The formula section should generally contain a formula for a(p^e) when this is not hard to define.
- new: This keyword denotes a sequence which has recently been added to the encyclopedia. Like keyword:changed, it is automatically added by the server when it applies.
- nice: Generally new submissions should not be given keyword:nice; instead, others propose it. See Andrew Weimholt, [9], posting to SeqFan on Nov 13 2009. When adding or removing the keyword a "pink box" comment should be added. See User:Charles R Greathouse IV/Keywords/aesthetic.
- nonn: This keyword should not be used when there are known to be negative members of the sequence, even if they do not appear in the sequence data. See Charles R Greathouse IV, [10], posting to SeqFan on Mar 25 2010.
- obsc: Introduced Jun 1998 for sequences where the definition is unclear. Little-used: should this and keyword:unkn be used more?
- probation: Introduced Mar 2006 and used only rarely since 2010. For sequences that may be deleted "at the discretion of the editor".
- recycled: Sequences which have been deleted and which will be reassigned later (soon). Introduced no later than Nov 2010. See keyword:new. See also Russ Cox, [11], posting to SeqFan on Nov 15 2010 (what is the keyword?) and Marc LeBrun, [12], posting to SeqFan on Jan 30 2011 ff. (should we recycle sequences at all?).
- sign: Sequences with negative terms. See keyword:nonn. Removed Jun 2002 but soon reinstated.
- tabf: Introduced July 1999 for tables with irregular row lengths—anything but 1, 2, 3, .... Is there a good way to store the shape of the sequence as metadata so it could be plotted? The most general solution would allow an arbitrary sequence (and offset) for the length of the rows.
- tabl: Regular tables, that is, tables with 1, 2, 3, ... members in each row. A general solution allowing a choice of shapes for tabf (q.v.) would suggest merging the two, making tabl just one of several special shapes.
- uned: Sequences which have been (provisionally) accepted but do not meet the usual editing standards. These should be brought 'up to code' and the keyword removed.
- unkn: A little-used keyword for sequences for which no definition is known, see N. J. A. Sloane, re open problems, posting to SeqFan on Feb 21 2009. Should this be used for sequences like A102241 and A100000 where the original meaning is lost? See keyword:obsc.
- walk: Little-used, and not present on many sequences that could use it. Really more like a tag or index link than the other keywords. This should be populated by someone with time and expertise.
- word: Sequences which depend on words in some language. Another tag-like keyword.

## Deprecated keywords

- done: Fl. 1999-2000, not currently in use.
- dupe: Introduced around 1999 and moribund since at least September 2007 when it was effectively replaced by keyword:dead.
- huge: Introduced by Feb 1997 and removed Jun 2002. For sequences that "contains terms too big for Fortran or C".
- look: Introduced by Feb 1997 and removed Feb 2002. For sequences which may be signed but do not have signed lines (%V, %W, %X). Note that the 2014 keyword look is unrelated.
- part: Removed Jun 2002 and rarely used. It was believed to have been created to mark partition-related sequences.

## Keyword compatibility

The following combinations are not permitted:

The following keywords should never appear with other keywords:

(Note: if a dead sequence has recently been added or modified, it will have new or changed; this is acceptable.) If none of the above standalone keywords are used, then exactly one of nonn and sign must be used.

The following keywords require other keywords:

Nonce and deprecated keywords should never be used, including in particular:

- done
- dupe
- huge
- part

## Combinatorics

With 34 keywords, there would normally be 2^34 = 17179869184 (≈17 billion) possibilities. But the restrictions above reduce the number of possibilities considerably.

First, there are 4 possibilities with the standalone keywords. Otherwise, the sequence must be either nonn or sign but not both, reducing the number to 4 + 2*2^28 = 536870916 (≈540 million). Since full requires fini, there are only three possibilities for both, lowering the total to 4 + 2*3*2^26 = 402653188 (≈400 million). Similarly tabl/tabf, nice/less, and easy/hard reduce the possibilities to 4 + 2*3^4*2^20 = 169869316 (≈170 million). Full and more are not permitted together, so considering fini, full, and more, there are 5 ways: none, more, fini, fini+full, and fini+more, giving a total of 4 + 2*3^3*5*2^19 = 141557764 possible assignments of keywords or just over 27 bits of information.

Of course very little of this space is actually used. There are fewer than 2000 different combinations currently in the OEIS, and even if each sequence was given its own unique combination this would explore only 0.2% of the entire space.

One of the reasons is that in this space the average sequence would have 13-14 keywords, while in the OEIS (as of Sep 17 2015) only one sequence has 8 and the rest have 7 or fewer. If the number was restricted to no more than 7 the number of possibilities would drop to less than a million.