[seqfan] Re: Sequence not in OEIS?

Giovanni Resta g.resta at iit.cnr.it
Thu Aug 22 08:40:30 CEST 2013


On 08/22/2013 03:14 AM, David Wilson wrote:
> When I calculate the sequence
> Smallest prime p where average gap between primes<= p is>= n
> Are my calculations wrong or is the sequence just not in the OEIS?

Your computation is correct. The sequence continues as

3, 11, 29, 127, 337, 1087, 3061, 8419, 23531, 64553, 175211, 480881,
1304503, 3523901, 9557957, 25874767, 70115473, 189961193, 514272413,...

Up to prime(k), average gap is actually equal to (prime(k)-2)/(k-1),
so this sequence is in spirit (and also in terms) very similar to
A038607, which is the sequence of smallest primes prime(k) for which
prime(k)/k >= n and begins with

2, 11, 37, 127, 347, 1087, 3109, 8419, 24317, 64553, 175211, 480881, 
1304707, 3523901, 9558533, 25874843, 70115473, 189961529, 514272533,...

Giovanni



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