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When I search a sequence in the OEIS and it's not there, it gives me a message saying "If your sequence is of general interest, please submit it using the form provided and it will (probably) be added to the OEIS!"

But I'm not always sure if I should. It's clear in cases when I made a mistake, I correct my mistake and the right sequence comes up; the OEIS does not need my erroneous version. But in other cases, it looks like my computations are totally correct and the sequence is not in the OEIS, but I'm not sure it's really worth adding, and that thing about "general interest" sounds kind of vague, plus there are some sequences in the OEIS that seem like they're of interest only to a very small group of specialists.

What criteria would you suggest to apply to a particular sequence to help me decide about submitting it one way or the other?

P.S. Something that occasionally happens is that it will tell me something like "Your sequence appears to be: $+ 20 x + 3 $. (I searched for "23,43,63,83,103,123,143").

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I think the best criterion is whether or not you're willing to explain or even defend your sequence. They're more polite at the OEIS, but if they can't see the point of your sequence, they will let you know.

For example:

Semiprimes $q$ such that $q + d$ is also a semiprime, where $d$ is the largest digit of $q$.

That was rejected, even though it's very similar to

A245742 Primes $p$ such that $p + d$ is also prime, where $d$ is the largest digit of $p$.

which was accepted. Sloane himself wrote:

This seems very artificial. Semiprimes are much less interesting than primes, and even for primes the concept seemed not so interesting.

The contributor was given time to defend, but he stayed quiet, so two other editors put the final nails on that coffin.

But if the sequence you want to add appears in a published book or journal, they're much more likely to accept it even if otherwise they would consider it boring.

(Just in case you're wondering, I'm not the contributor of either of those. Every time I think I have a sequence worth adding to the OEIS, turns out I made some little mistake and the sequence has been in the OEIS, like, from the very beginning).

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    $\begingroup$ I like this example because it refutes the slippery slope argument. If the OEIS accepts one sequence of a given kind, there is no obligation to also accept every possible variation. $\endgroup$
    – user153918
    Aug 11, 2014 at 19:23
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    $\begingroup$ So that's why the OEIS doesn't have the decimal expansion of $\sqrt[71]{7531894202}$! $\endgroup$ Aug 11, 2014 at 22:33
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The criterion that I suggest is this: Do you think your sequence would be useful to someone else if it came up in their search results? Would they feel grateful for the information that you put in the entry? The nice thing about the OEIS is when it helps you make unexpected connections, such as if a sequence that you defined one way can also be defined in a different and seemingly unrelated way.

But if that's still not enough to help you make your decision, I suggest you read Charles Greathouse's essay on what makes a sequence interesting. I've also written one of those (Charles is an Editor-in-Chief at the OEIS, I'm an Associate Editor). They are guidelines, not rules. It could happen that after you read those, you think that your sequence does belong in the OEIS even if the essays suggests that it doesn't. But then you might be better able to explain why it does belong.

The reason we don't want to set rigid rules for this kind of thing is that we don't want to paint ourselves into a corner, such as if someone sends in a sequence that's really interesting but the rules dictate it should be rejected, or a very uninteresting, useless sequence which the rules dictate should be accepted.

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I would submit any sequence related to typical analytic maneuvers and forms that lie in the intersection of diverse fields of mathematics. For example, in dynamical systems, nonlinear PDEs, complex calculus, and differential geometry, the Schwarzian derivative frequently pops up and can be represented quite simply in terms of a convolution of the Faber polynomials (cf. OEIS A263646). In algebraic geometry, special functions, group theory, differential topology, and operator calculus, the various classes of symmetrc polynomials play special roles, so any array related to non-trivial transformations between the classes should be submitted (cf. A036039).

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