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A257648 Numbers m such that both p=2*m^2+11 and q=2*p^2+11 are prime. 1

%I #16 Jun 16 2022 17:58:27

%S 1,2,3,4,6,7,8,13,20,31,52,54,62,65,70,75,137,151,153,163,212,224,281,

%T 284,329,384,419,424,445,455,489,505,524,581,593,642,646,680,706,723,

%U 738,746,775,787,795,830,841,843,918,953,970,973,984

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

%C 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.

%H Harvey P. Dale, <a href="/A257648/b257648.txt">Table of n, a(n) for n = 1..1000</a>

%e n=1: m=1=A092968(2) and p=13=A092968(12),

%e n=8: m=13=A092968(12) and p=349=A092968(127),

%e n=9: m=20=A092968(12) and p=811=A092968(251).

%t Reap[Do[If[PrimeQ[p=2*k^2+11]&&PrimeQ[2*(p)^2+11],Sow[k]],{k,10^3}]][[2,1]]

%t bprQ[n_]:=Module[{p=2n^2+11},AllTrue[{p,2p^2+11},PrimeQ]]; Select[Range[ 1000],bprQ] (* _Harvey P. Dale_, Jun 16 2022 *)

%Y Cf. A050265, A092968.

%K nonn

%O 1,2

%A _Zak Seidov_, Jul 25 2015

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)