A144103 Let N(p,i) denote the result of applying "nextprime" i times to p; a(n) = smallest prime p such that N(p,2) - p = 2*n, or -1 if no such prime exists.

-1, 3, 5, 23, 19, 47, 83, 211, 109, 317, 619, 199, 1373, 1123, 1627, 4751, 2557, 3413, 4289, 1321, 2161, 2477, 7963, 5591, 9551, 17239, 15823, 14087, 19603, 34963, 36389, 33223, 24251, 35603, 43321, 19609, 134507, 31393, 136999, 31397, 38461, 107357

Offset: 1

Author

T. D. Noe, Sep 11 2008

Keywords

• sign

Comments

p and p+2n are primes and there is one prime in the range p+1 to p+2n-1.

a(n) is the prime for which 2n+2 first occurs in A031131.

Links

• Martin Raab, Table of n, a(n) for n = 1..469 (terms 1..342 from Robert G. Wilson v)
• Mersenne Forum, Gaps between non-consecutive primes

Crossrefs

Cf. A031131.

A000230 is an analogous sequence based on N(p,1). - N. J. A. Sloane, Nov 07 2020

Programs

Mathematica

nn=51; t=Table[0,{nn}]; t[[1]]=-1; cnt=1; n=1; While[cntHarvey P. Dale, Jun 26 2017 *)

Extensions

Definition edited by N. J. A. Sloane, Nov 07 2020