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

1,2

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..408 (Terms 1..342 from Robert G. Wilson)

Mathematica

nn=51; t=Table[0, {nn}]; t[[1]]=-1; cnt=1; n=1; While[cnt<nn, n++; d=(Prime[n+2]-Prime[n])/2; If[d<=nn && t[[d]]==0, cnt++; t[[d]]=Prime[n]]]; t=Rest[t]
Flatten[Table[Select[Partition[Prime[Range[20000]], 3, 1], #[[3]]-#[[1]] == 2n+2&, 1], {n, 41}], 1][[All, 1]] (* Harvey P. Dale, Jun 26 2017 *)

Crossrefs

Cf. A031131.

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

Sequence in context: A270209 A271464 A088121 * A270155 A271308 A270163

Adjacent sequences: A144100 A144101 A144102 * A144104 A144105 A144106

Keyword

sign

Author

T. D. Noe, Sep 11 2008

Extensions

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

Status

approved