Primefree sequences in the OEIS. A bad idea.

[Alonso Del Arte]

If you were doing a competitor database to the OEIS, then it would be
a good idea to avoid this sort of self-referential sequence, at least
early in the history of the project. But the OEIS, with its longevity,
authoritativeness and widespread admiration, has earned the right to
the occasional self-reference, and some self-referential sequences are
thought up by several different persons independently. Even today
there must be people who think about submitting the delightfully
paradoxical sequence "An does not contain n", and find it's already
there, and I'm surprised no one had thought of A111157 before, it
could have been submitted as early as 1995.

I find the idea of A111157 interesting because primes are hard to
avoid. I can only think of three kinds of sequences that are
guaranteed not to contain primes: n-gonal numbers (for composite n),
multiples of n (for composite n) and nth powers (for n > 1). Even the
sequence of highly composite numbers has a prime. The first primefree
linear recurrence sequence to be discovered was Graham's 1964 a(1) =
331635635998274737472200656430763, a(2) =
1510028911088401971189590305498785, and it wasn't until years later
that such sequences with smaller initial terms were found.

Al

On 10/24/05, David Wilson <davidwwilson at comcast.net> wrote:
> As an editor, I opine that sequences in which a(n) depends on sequence
> numbers (A,M,N-numbers) do not belong in the OEIS.  Such sequences are of
> marginal interest, no utility, and are difficult to maintain. Were it my
> database, I would prohibit adding any new sequences of this sort, and would
> cull the existing ones (A051070, A031214, et al).
>
>