User:Charles R Greathouse IV/Is this sequence interesting

This essay is a response to User:Alonso del Arte/Is this sequence interesting containing my own views on the interestingness and, more to the point, appropriateness of sequences. Its purpose is to communicate my thoughts and promote discussion, not to set a standard for the OEIS (which comes rather through a consensus of the Editorial Board).

Interesting, probably should be in the OEIS

• A simple function or procedure leads to unexpected results.
• A neat illustration of a beautiful or well-known theorem.
• A new result from the literature.
• Apparently unrelated processes generate the same sequence.
• You can prove a nontrivial property of a simple function or procedure.

Interesting, probably not for the OEIS

• Sequences already in the OEIS, or essentially identical to an existing sequence. (Please add any new information to that sequence.)
• Sequences with fewer than three terms. See User:Charles R Greathouse IV/Keywords#bref.

Not interesting, not for the OEIS

These are generally inappropriate for the OEIS. The characteristic that sets them apart is a lack of motivation: the sequences set out a set of steps to follow but not why they should be followed.

• Arbitrary transformations of sequences with no relationship between the sequence and transformation.
  • For example, consider A083393, "Palindromes such that the sum of the digits is prime". This sequence is presumably interesting, having been accepted into the OEIS. But its Boustrophedon transform would probably be rejected, because there's no reason to apply that transform to the sequence.
• Sequences with many free parameters and/or arbitrary large constants. This can be quantified better than most: how many distinct sequences can be formed with parameters less than or equal to the current choices? If this is large, the sequence should generally be rejected unless there is special meaning in the specific choice of parameters.
  • The powers of two is a good sequence, but the powers of 1652 is not.
  • Consider a linear recurrence of signature (4, -4, 0, 2) and starting values 1, 4, 1, 4. There are 8 parameters in the range [-4, 4] for a total of roughly 9⁸ possible sequences of this form. Unless there is special meaning behind these choices the sequence should be rejected. (Of course sequences with good motivation are welcome, regardless of whether they have a closed-form recurrence or not.)
• The composition of apparently-unrelated sequences or functions applied to n. f(n) and f(g(n)) are probably fine, but f(g(h(n))) and f(g(h(i(n)))) should be reserved for very unusual cases.
  • The sum of the digits of sopfr(n^3 + 1) would probably be rejected, without some connection between $\scriptstyle n\mapsto \operatorname {dsum} (n),n\mapsto \operatorname {sopfr} (n),n\mapsto n^{3}+1.$
• Generally, a very complicated function or procedure which leads to somewhat predictable results.

Not interesting, probably not for the OEIS

These are generally inappropriate for the OEIS. But in some cases, applied to important sequences, they may be acceptable.

• Small modifications of existing sequences.
• Uncommon or uninteresting transformations, unless strongly motivated.
  • The binomial transform and Möbius transform apply naturally to many sequences. But some, like DHK_k or DELTA, are more specialized and should mostly be applied to give a pointer to the transformation itself. (Using the "free parameters" test above, these should be considered as members of a large collection of transformations adding a large amount of arbitrariness to sequences.)
  • Of course there are cases where the transformations are relevant and appropriate. Be sure to (1) explain the transformation, which may not be known (or may not be known by the same name) to the reader, and (2) explain the relevance of the transformation. If a sequence is called, e.g., Fooian transform of the triangular numbers, add a comment The fooian transform gives the number of ways to arrange a sequence in 2-space, hence this is the number of ways to build a wall out of triangular bricks. (In that case the comment and name might be reversed.)
• Characteristic functions of other sequences.
  • These are generally added only when (1) the underlying sequence is well-known and (2) the characteristic sequence has some special interest.
• Sequences not of general interest, or tied to some specific place or time.

Not interesting but maybe should be in the OEIS

These are bread-and-butter sequences: too important to leave out, even if there isn't much to say.

• Very predictable but useful sequences. Sequences in this category should only very rarely be accepted, since most sequences of this kind are already in the OEIS.
• Sequences very similar to an existing sequence, but which differ sufficiently that this sequence might show up in a search but not the original.
  • Generally this is appropriate only where the existing sequence is a core sequence or otherwise especially important.
• Sequences that appear in the literature, and...
  • ...are erroneous. An entry should be added to point to the correct version.
  • ...are correct. If there is related work to point to, adding a sequence may be appropriate even if the sequence is not a priori interesting. Someone might look it up in hopes of finding more on the topic.
• Simple compositions and transformations of core sequences, when there is at least some relationship. Not every sequence should have a "prime in A..." sequence, but this is appropriate for some very basic sequences.

General principles

Sequences which are interesting of their own right or which come up naturally in research are generally accepted. Sequences which are invented purely for the purpose of adding a sequence to the OEIS are generally rejected. In favor of inclusion:

• Nontrivial properties have been proved
• Two or more not obviously equivalent definitions
• Appears in a peer-reviewed publication
• Came up in your research, and is likely to come up in others'

See also

• Examples of what not to submit
• User:Alonso del Arte/Is this sequence interesting
• User:Charles R Greathouse IV/Imp

External links

• How to Create a New Integer Sequence
• Robert Munafo, Is this sequence interesting?
• Ralf Stephan, Random 100 sequences from the OEIS—a survey
• Randall Munroe, OEIS Submissions (comic)