Primefree sequences in the OEIS. A bad idea.

[Alexandre Wajnberg]

> 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 agree: the historical aspect of OEIS is worth to be considered, at least
for *some* seqs such as "generic" ones (among them "diagonal" ones for
instance) because OEIS is not only a "pure maths" tool, but also shares game
aspects (sequences linked to games), musical aspects, displays sequences
which are not purely mathematical ones (like those describing biological or
physical realities or human realizations), or even expresses humorous
aspects. It's a matter of balance: once an interesting "not pure math" idea
has been posted, we may avoid the variations on the same theme.

Generally speaking, we should take care, through those OEIS-referring
sequences (which are not truly self-referring ones!) not to remake other
versions of the lexicographic order, or of pages which list sequences having
particular features (like Michael Gilleland's "Some Self-Similar Integer
Sequences").

> 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).


I would also add the sequences which *by definition* exclude primes (they
are obvious but they exist!) such as A110095: "Least increasing sequence of
nonprimes whose first differences are also nonprime."
There must be a lot of them, isn't it?

Alexandre