A182315 Primes prime(n) such that prime(n+1) - prime(n) > log(n)^2.

2, 3, 5, 7, 13, 23, 31, 113, 1327, 31397, 370261, 492113, 2010733, 20831323, 25056082087, 42652618343, 2614941710599, 19581334192423

Offset

1,1

Comments

Using terms of A002386, a(19) is probably 218209405436543. - T. D. Noe, Apr 24 2012

Links

Table of n, a(n) for n=1..18.

Mathematica

t = {}; Do[If[Prime[n + 1] - Prime[n] > Log[n]^2, AppendTo[t, Prime[n]]], {n, 10000}]; t (* T. D. Noe, Apr 24 2012 *)

Prog

(PARI) n=0; G=1; p=2; forprime(q=3, 1e8, n++; if(q-p>=G&&q-p>log(n)^2, G=ceil(log(n)^2); print1(p", ")); p=q) \\ Charles R Greathouse IV, Apr 24 2012

Crossrefs

Subsequence of A211073.

Cf. A002386, A134266.

Sequence in context: A064336 A179921 A211073 * A233862 A235394 A126092

Adjacent sequences: A182312 A182313 A182314 * A182316 A182317 A182318

Keyword

nonn,hard,more

Author

Thomas Ordowski, Apr 24 2012

Extensions

a(13)-a(16) from Charles R Greathouse IV, Apr 24 2012

a(17) from Charles R Greathouse IV, Apr 26 2012

a(18) from Charles R Greathouse IV, May 06 2012

Status

approved