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%I #3 Mar 31 2012 12:38:24
%S 8981279,17313839,18635759,82062479,82479119,98517599,112242479,
%T 113164319,152799359,184829279,193409039,230749199,296709839,
%U 305598719,339116159,393280799,406283519
%N Triple-safe primes which are also triple-Sophie Germain primes.
%C The intersection of the primes in A157358 and those in A023272: they remain prime after each
%C of three successive applications of the substitution p->(p-1)/2, and remain prime after each
%C three successive applications of the substitution p->2p+1. Therefore the sequence is a subsequence
%C of A162019.
%C They appear for example in the middle of chains started in A059767 or in even longer Cunningham chains. [_R. J. Mathar_, Jun 26 2009].
%t f[n_]:=Module[{x},If[PrimeQ[(n-1)/2]&&PrimeQ[(((n-1)/2)-1)/2]&&PrimeQ[(((((n-1)/ 2)-1)/2)-1)/2]&&PrimeQ[2*n+1]&&PrimeQ[2*(2*n+1)+1]&&PrimeQ[2*(2*(2*n+1)+1)+1], x=1,x=0];x]; lst={};Do[p=Prime[n];If[f[p]!=0,AppendTo[lst,p]],{n, 6*10!}];lst
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 25 2009
%E Edited by _R. J. Mathar_, Jun 26 2009
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