A257648 Numbers m such that both p=2*m^2+11 and q=2*p^2+11 are prime.

1, 2, 3, 4, 6, 7, 8, 13, 20, 31, 52, 54, 62, 65, 70, 75, 137, 151, 153, 163, 212, 224, 281, 284, 329, 384, 419, 424, 445, 455, 489, 505, 524, 581, 593, 642, 646, 680, 706, 723, 738, 746, 775, 787, 795, 830, 841, 843, 918, 953, 970, 973, 984

Offset: 1

Author

Zak Seidov, Jul 25 2015

Keywords

• nonn

Comments

Numbers m such that both m and p=2*m^2+11 are terms in A092968. Also, both p and q are terms in A050265.

Examples

			n=1: m=1=A092968(2) and p=13=A092968(12),
n=8: m=13=A092968(12) and p=349=A092968(127),
n=9: m=20=A092968(12) and p=811=A092968(251).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A050265, A092968.

Programs

Mathematica

Reap[Do[If[PrimeQ[p=2*k^2+11]&&PrimeQ[2*(p)^2+11],Sow[k]],{k,10^3}]][[2,1]]
bprQ[n_]:=Module[{p=2n^2+11},AllTrue[{p,2p^2+11},PrimeQ]]; Select[Range[ 1000],bprQ] (* Harvey P. Dale, Jun 16 2022 *)