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User talk:Charles R Greathouse IV/Keywords

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A table of suggested new keywords (and a new keyword organizational structure) is here: User:Charles R Greathouse IV/Keywords/Table. Discussion is at User talk:Charles R Greathouse IV/Keywords/Table.

Suggestions for new keywords

  • conj: sequence is only conjectured to be correct (Examples: A023108, A051021, A101036)
  • perio: sequence eventually starts to repeat periodically at some point (Examples: A010690, A244550)
    What about perio[pre: k; per: l], where k is the number of terms of the prefix, l is the period length. — Daniel Forgues 01:14, 25 March 2015 (UTC)
In my opinion that information should be added to the comments in order to avoid 'keyword clutter', but maybe that's just me. Felix Fröhlich 13:29, 13 April 2015 (UTC)
  • infi: sequence is proven to be infinite (Examples: A000040, A016789)
  • nonprim: any term of the sequence is either 1 or composite and sequence contains the term 1 at least once (Examples: A014076)
    Does it admit 0, −1 and "negative" composites? — Daniel Forgues 01:14, 25 March 2015 (UTC)
    I would say it should, though that might return some potentially unwanted sequences when using the keyword in search queries. Not sure if there is a way to tell the search engine not to return sequences with a particular keyword. If there were, searching only for sequences with positive primes could be done by using something like keyword:nonprim !keyword:sign (don't know if there is an expression for the NOT operator in search queries). Felix Fröhlich 13:32, 19 May 2015 (UTC)
    Why does it need the term 1? — Douglas Boffey 15:17, 18 February 2016 (UTC)
    My idea was that when 1 is not a term it should have keyword compo instead. So there would be different keywords for sequences of composites (not including 1) and sequences of nonprimes (since 1 is neither prime, nor composite). Felix Fröhlich 22:17, 6 March 2016 (UTC)
  • compo: any term of the sequence is composite (Examples: A001567, A002808, A002997)
    Does it admit "negative" composites? — Daniel Forgues 01:14, 25 March 2015 (UTC)
  • monoinc: a monotonically increasing sequence (Examples: A002024)
  • monodec: a monotonically decreasing sequence (Examples: A168050)
  • strinc: a strictly increasing sequence (Examples: A000027)
  • strdec: a strictly decreasing sequence (Examples: A096582)

(regarding the last four, I only just saw Daniel Forgues suggestion from 2011-02-06)

Felix Fröhlich 07:24, 27 October 2014 (UTC)

  • prim: all terms of the sequence are primes
    Does it admit "negative" primes? — Daniel Forgues 01:14, 25 March 2015 (UTC)
  • nond: non-decreasing sequence: a(n+1) >= a(n)
    Is there a difference between this and monoinc? — Douglas Boffey 15:17, 18 February 2016 (UTC)
  • nodu: no duplicates in the sequence: a(m)!=a(n) if m!=n, every integer appears at most once
  • perm: the sequence is a permutation of natural numbers

Alex Ratushnyak 28 December 2013

  • add: additive sequences (a(mn) = a(m) + a(n), (m,n) = 1)
  • compadd: completely additive sequences (a(mn) = a(m) + a(n))
  • compmult: completely multiplicative sequences (a(mn) = a(m) * a(n))
  • div: divisibility sequences (m | n implies a(m) | a(n))

Daniel Forgues 01:40, 3 February 2011 (UTC)

Yes. I mostly talk about those at User:Charles R Greathouse IV/Metadata but I'll get around to mentioning these here, along with some others I'd like to see.
Of course it's not obvious what the best system for categorization is, in general. I like the idea of using several systems:
  • Keywords for major immutable properties of sequences
  • Tags for amorphous things like topic
  • Indexes for connections between small groups of sequences (including non-obvious groupings like 'sequences related to complexity'
  • 'See also' for connections between individual sequences
So from that perspective I'd like to see just a small number of additional keywords, maybe just half a dozen. I think it's best that we have real community discussion about this -- they're hard to change once set up.
Charles R Greathouse IV 05:36, 3 February 2011 (UTC)
If we could have an editable hierarchical category system like in OEIS Wiki (originally the sequences were categorized in the Wiki) this would be much better than the flat (non-hierarchical) limited set of pre-approved abbreviated keywords system. — Daniel Forgues 04:28, 4 February 2011 (UTC)
I talk about that on my Metadata page under the name "tags".
To get more into specifics: I'd like to see keywords for additive sequences, divisibility sequences, linear recurrence relations, and possibly some others. I think that the 'right' way to handle completely multiplicative|additive functions is to subtype the keywords:
 %K sign,mult(completely),nice
just like I'd like to see
 %K nonn,base(10)
Charles R Greathouse IV 06:20, 4 February 2011 (UTC)
  • nestrad(2): a nested square radicals expansion of a number
  • nestrad(3): a nested cubic radicals expansion of a number

Daniel Forgues 07:08, 4 February 2011 (UTC)

This is a large category, because prime-indices can be used to encode not just integer partitions (those counted by A000041), but also nonoriented rooted trees (those counted by A000081), via Matula-Goebel encoding. Maybe these could be further separated:

  • pind.intpart
  • pind.matulagoebel
  • pind.recurrence


  • perm.binwords: sequence is a bijection on binary words (one that preserves their size), meaning that no cycle will cross over boundaries set by A000225 and A000079. Maybe two keywords, perm and base.fix.2 would together indicate the same? (Examples: A003188, A153141, A193231)
  • perm.catalanbij: sequence is a "signature-permutation" of an automorphism/bijection acting on combinatorial structures (e.g. ordered binary trees, Dyck paths) in Catalan families, ordered by convention as in A014486 (Examples: A057163 and about 500 other sequences with /index/Per#IntegerPermutationCatAuto in their %H-field)

Antti Karttunen 11:04, 23 February 2015 (UTC)

Comments on nond: I think that this should be a really useful keyword, which actually is applicable to a great proportion of all sequences. However, it should be clarified whether the non-decreasing property would refer to just the known terms, or (for theoretical reason) to all terms. I think that the latter sense should be chosen. Whether or not just all known and listed terms form a non-decreasing sequence might be deductible automatically; but the fact that also the unknown terms satisfy a(n+1) >= a(n) adds real knowledge about the sequence.
Jörgen Backelin 00:58, 13 January 2016 (UTC)

Daniel Forgues 22:06, 24 February 2017 (UTC)

  • tinf: sequence tends to +∞ as n → ∞
  • tminf: sequence tends to -∞ as n → ∞

Douglas Boffey 15:46, 18 February 2016 (UTC)

  • 1to1: one-to-one sequences;

Daniel Forgues 19:07, 26 May 2018 (EDT)

Dotted keywords

What about using dot notation for subkeywords?

  • frac(num) or frac.num: fractions numerators
  • frac(den) or frac.den: fractions denominators
  • cfrac.conv.num: continued fractions convergents numerators
  • cfrac.conv.den: continued fractions convergents denominators

Daniel Forgues 06:18, 5 February 2011 (UTC)


  • mono.decr: monotonic decreasing sequences
  • mono.decr.strict: monotonic strictly decreasing sequences
  • mono.incr: monotonic increasing sequences
  • mono.incr.strict: monotonic strictly increasing sequences
  • base.fix.1.Roman Roman numerals dependent sequences
  • base.fix.2 base 2 dependent sequences
  • base.fix.3 base 3 dependent sequences
  • base.fix.bal.3 base 3 (balanced) dependent sequences
  • base.fix.10 base 10 dependent sequences
  • base.mix.fact mixed base (factorial) dependent sequences
  • base.mix.prim mixed base (primorial) dependent sequences
  • infinite sequences
  • conjectured infinite sequences
  • fini?: unknown whether finite or infinite sequences
  • fini.yes?: conjectured finite sequences
  • fini.yes: finite sequences
  • fini.N: N terms finite sequences

Daniel Forgues 03:45, 6 February 2011 (UTC)

For technical reasons I'd prefer a dash to a dot—it would allow |= selectors.
If we were to use some version of that notation I would say mono-decr / mono-incr / mono-cons (for sequences like A010727 that are nondecreasing and nonincreasing), with -strict for the former two. (I wish mono-incr-strict was less verbose, since it will be very common. I don't suppose anyone has a better suggestion here?)
fini-N should probably be fini-yes-N so they come up in a search for keyword:fini-yes.
I would prefer to make fixed integer bases the default and put others under a subkeyword: base-10 but base-mixed-fact and base-other-phinary (I'm open to suggestions on the best subkeywords here, I don't like "other").
I don't like cofr-conv (you wrote "cfrac.conv") because they're fractions, not continued fractions; that they're derived from continued fractions does not seem like something keywords should encode. They are fractions, but they're related to continued fractions. "Related to" is the function of an index, not of keywords, IMO.
Charles R Greathouse IV 22:00, 6 February 2011 (UTC)

Franklin T. Adams-Watters 10:02, 20 February 2015 (UTC)

I prefer the parentheses over either of these. This lets me write "add(conj,comp)" for a sequence that is conjectured to be additive, and in fact completely additive, while "add(comp(conj))" would identify a sequence known to be additive, but for which it is only conjectured that it is completely additive.
In this notational system, what is supposed to be what? For example, if "prim" denotes a sequence where all terms are prime and for a sequence it is only conjectured (but not proven) that all terms are prime, would that sequence get "prim(conj)" or "conj(prim)"? Felix Fröhlich 13:40, 13 April 2015 (UTC)

I would like to see a modifier abs, meaning the property only applies to the absolute values — Douglas Boffey 15:35, 18 February 2016 (UTC)

About keyword: base

I think we should have two distinct keywords to distinguish between the following two meanings:

Sequences that are really dependent on the numeral representation of the numbers, not just superficially different depending on the choice of numeral system the represent the sequence, e.g.
Palindromic primes (i.e. Palindromic primes (base 10)) vs Palindromic primes (base 2)
Repunit primes (i.e. Repunit primes (base 10)) vs Repunit primes (base 2)
Sequences that only happen to be represented in a numeral system other than the default numeral system (i.e. base 10), e.g.
Prime numbers (i.e. Prime numbers (base 10)) vs Prime numbers (base 2)

The sequence of prime numbers modulo the representation is unique, so the sequences expressing the prime numbers in different bases are only superficially different. Maybe we should use keyword: repr-2 for example to express the fact that the sequence is represented in base 2.

The sequence of Palindromic primes (base 2), if converted to base 10, would not be the sequence of Palindromic primes (base 10) because the sequences are essentially different, not just in their representation. So the keywords: base-2, repr-2 would apply to Palindromic primes (base 2) if represented in base 2.

To further distinguish the two meanings, consider Palindromic primes (base 2), expressed in base 10, where we could be using the 2 keywords: base-2, repr-10.

Daniel Forgues 06:48, 13 February 2011 (UTC)
I generally don't think we should have sequences represented in other bases at all. (Rather, a sequence should be able to be displayed in an arbitrary base as needed.) So I don't see the need for the 'repr' keyword.
Of course there are sequences like A007088 that can be described as being represented in other bases, but for which there are alternate descriptions (sums of distinct powers of 10).
Charles R Greathouse IV 06:55, 13 February 2011 (UTC)

Should A182979 have keyword: base? I don't think so, but other editors do think so. It is using base 2 for its representation, but it expresses base-independent properties of numbers. — Daniel Forgues 07:13, 13 February 2011 (UTC)

I've considered (in the past, not so much recently) a keyword, perhaps 'symb', for sequences where the digits should be read as tally-marks, distinct but otherwise arbitrary objects, etc. If we had such a keyword that would apply here rather than base. Charles R Greathouse IV 19:05, 13 February 2011 (UTC)


My guess for keyword:part: sequences having to do with partitions. But I haven't seen any evidence of that keyword, probably since it was deprecated before I even knew about the OEIS. Alonso del Arte 05:41, 7 February 2013 (UTC)

Just in case, this is now covered by the part redirection to Clear-cut_examples_of_keywords#dupe intended for the DRAFT version of dupe, but I'm not confident that any drafts make it to non-draft in a timely manner (= at most 7 days for watch lists) here. –Frank Ellermann 16:29, 13 November 2017 (UTC)

full and unkn

About the keyword "full": I agree to changing the meaning (so now it will include the terms in the b-file as well as those in the DATA field)
When this keyword was introduced there were no b-files.
in reply to my message:
It appears that "full" should only be used when all terms are in the 3 lines.
I am not sure whether this is the best choice. I think when a b-file with the complete sequence is given, then it should be considered as "full", too. Else, the "full" property depends on our completely arbitrary choice of how many terms should be displayed *by default* (and/or respecting guidelines...).
It seems obvious to me that such is extremely bad practice. In particular, I would like / suggest / am sure that sooner or later, each user can choose through his personal preferences, how many terms (s)he wants to have displayed (1 line, 3 lines,...), especially in search results (and or depending on the user agent: mobile device,...)(comment added later). Then this use of "full" becomes even more non-sensical.
  • about "unkn", AFAIK, this rather marks sequences where serious mathematical questions remain unsolved (finitude, conjectures, ...)

M. F. Hasler 22:02, 12 February 2013 (UTC)

I agree on full and will update soon (perhaps following a move to implement this?).
I disagree on unkn. When this last came up on SeqFan Franklin TAW wrote:
My understanding of the "unkn" keyword is that the sequence itself is unknown or very poorly understood. It doesn't mean any sequence for which there is an open conjecture.
and Neil agreed, writing:
Yes, officially it means that no-one knows how the sequence is defined
So I think that's fairly explicit.
Charles R Greathouse IV 00:16, 13 February 2013 (UTC)


Perhaps some of these:

PRBS - pseudo-random binary sequence
PRS - pseudo-random sequence
PRNG - pseudo-random number generator (related to)

The definition would have to be very clear, as to mean and pair sum distributions at the least. A010060, A014577 and A205083 all display mean=0.5 but while the latter 2 show pair sum distribution 1/2/1 as with a coin flip, Thue-Morse shows 1/4/1. --Bill McEachen 20:34, 22 March 2015 (UTC)

Keyword compatibility

Shouldn't there be "cons requires nonn"? --Andrey Zabolotskiy 11:17, 1 December 2016 (UTC)

Good point, thanks! I've added it. Charles R Greathouse IV 21:53, 1 December 2016 (UTC)


IIRC done was something like "approved" (by an editor) and ready for inclusion, i.e., the 2nd state after uned. –Frank Ellermann 07:04, 13 October 2017 (UTC)

done now goes to Clear-cut_examples_of_keywords#dupe intended for the DRAFT version of dupe. –Frank Ellermann 16:37, 13 November 2017 (UTC)