A225747 a(n) = smallest prime q > a(n-1) such that 2*prime(n)*q^prime(n)+1 is also prime.

2, 3, 7, 17, 1579, 1997, 2347, 3323, 6637, 11161, 13829, 18287, 40759, 42197, 42337, 45757, 46141, 48383, 49253, 51631, 52541, 53549, 73477, 78079, 81677, 111439, 164363, 166567, 170441, 180667, 191507, 202729, 209029, 257351, 292471, 294809, 300569, 328787

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..177

Example

2*2*2^2+1=17 prime so a(1)=2,
2*3*2^3+1=49 composite,
2*3*3^3+1=163 prime so a(2)=3 as 3>2.

Mathematica

nxt[{n_, a_}]:=Module[{p=NextPrime[a], c=Prime[n+1]}, While[!PrimeQ[ 2*c*p^c+1], p = NextPrime[ p]]; {n+1, p}]; NestList[nxt, {1, 2}, 40][[All, 2]] (* Harvey P. Dale, Jul 03 2021 *)

Prog

(PFGW & SCRIPTIFY)
SCRIPT
DIM n, 0
DIM k, 0
DIM q
DIMS t
OPENFILEOUT myfile, a(n).txt
LABEL a
SET n, n+1
IF n>177 THEN END
LABEL b
SET k, k+1
SET q, p(k)
SETS t, %d\,; q
PRP 2*p(n)*q^p(n)+1, t
IF ISPRP THEN GOTO c
GOTO b
LABEL c
WRITE myfile, q
GOTO a

Crossrefs

Cf. A225403.

Sequence in context: A102226 A195530 A295509 * A058334 A303090 A131093

Adjacent sequences: A225744 A225745 A225746 * A225748 A225749 A225750

Keyword

nonn

Author

Pierre CAMI, May 14 2013

Status

approved