[seqfan] minor correction of A000230

Russell Webb nthlab at gmail.com
Wed Aug 18 14:08:52 CEST 2021


https://oeis.org/A000230
For A000230, the description is "a(0)=2; for n>=1, a(n) = smallest prime p
such that there is a gap of exactly 2n between p and next prime, or -1 if
no such prime exists."

I take that to mean that there is no proof that such a prime exists for all
n, and the sequence might contain -1.  However, the sequence has the "nonn"
keyword.

Possible corrections:
a. such a p can be proven to exist, so the "or -1 if no such prime exists"
can be removed.  Likely true but possibly hard to prove.
b. change to "or 0 if no such prime exists"
c. remove the "nonn" keyword

On a related note, is it advisable to have a fall back clause for sequences
that are not proven to exist for some n?  Or should they be marked as such
with something like "posfin", possibly finite, or "posundef" possibly
undefined (I don't see a suitable keyword).

Cheers,
Russ



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