[seqfan] Re: Sequence not in OEIS?

[L. Edson Jeffery]

>When I calculate the sequence

>Smallest prime p where average gap between primes <= p is >= n

>I get

>3,11,29,127,337,...

>indexed starting at n = 1.  Are my calculations wrong or is the sequence
just not in the OEIS?


Very nice sequence! The terms listed are correct (verified by hand) and not
in OEIS. A couple of comments:

For reference, the gaps are A001223 <http://oeis.org/A001223>, and their
partial sums are A040976 <http://oeis.org/A040976> in which

A040976(n) = A000040 <http://oeis.org/A000040>(n)-2.

We at least have to have p > m^2, for some m >= n, so the largest m such
that your a(n) > m^2 is the sequence

1,3,5,11,18,...

These are the first five terms of A070316 <http://oeis.org/A070316> which
is probably not related (I did not explore it further). Finally, the
sequence of indices of your a(n) (in A00040) is

2,5,10,31,68,...

Ed Jeffery