A211073 -id:A211073 - cp's OEIS frontend

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

Thomas Ordowski, Apr 24 2012

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

Subsequence of A211073.

Cf. A002386, A134266.

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

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

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

A211075 Primes p followed by prime gap of length log(p/log(p)^2)^2.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 233, 241, 251, 257, 263, 271, 283, 293, 317, 331, 337, 353, 359, 367, 373, 383, 389, 401, 409

Offset: 1

Charles R Greathouse IV, May 06 2012

nonn

Primes followed by unusually long prime gaps.

Charles R Greathouse IV, Table of n, a(n) for n = 1..4139

Cf. A211073, A002386, A082885, A111943, A182315.

Select[Prime[Range[200]], NextPrime[#] - # > Log[#/Log[#]^2]^2 &] (* Alonso del Arte, Jun 02 2013 *)

G=1;p=3;forprime(q=5,1e7,if(q-p>=G,G=log(p/log(p)^2)^2; if(q-p>=G, print1(p", ")));p=q)

cp's OEIS Frontend

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

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