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A162019 Double-safe primes which are also double-Sophie Germain primes. 2

%I #8 Jun 23 2021 07:38:34

%S 11,359,719,214559,215399,245639,253679,266999,507359,508559,574439,

%T 670919,744599,825479,1017119,1072199,1184399,1363679,1621079,1688279,

%U 1786439,2156039,2377799,2429279,2633399,2684999,2900039,3103799

%N Double-safe primes which are also double-Sophie Germain primes.

%C The intersection of the primes in A066179 and those in A007700: they remain prime after each of two successive applications of the substitution p->(p-1)/2, and remain prime after each two successive applications of the substitution p->2p+1.

%F a(n) = 4*A023302(n) + 3 = (A157359(n)-3)/4. - _R. J. Mathar_, Jun 26 2009

%e a(1)=11 is double safe: (11-1)/2=5; (5-1)/2=2, and double Sophie-Germain: 2*11+1=23; 2*23+1=47.

%t lst={};Do[p=Prime[n];If[PrimeQ[safe=(p-1)/2],If[PrimeQ[(safe-1)/2],If[PrimeQ[sophie=2*p+1],If[PrimeQ[2*sophie+1],AppendTo[lst,p]]]]],{n,3*9!}];lst

%Y Cf. A007700, A023302, A066179, A157359.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jun 24 2009

%E Edited by _R. J. Mathar_, Jun 26 2009

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