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Sophie Germain primes in A154939.
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%I #6 Sep 21 2023 13:21:10

%S 3,5,11,131,419,1409,2069,3449,3761,3911,6899,7079,7151,9539,9791,

%T 10529,10691,11321,11831,14741,15269,17291,22079,27281,27809,30449,

%U 34439,45131,48479,52289,54251,64439,70901,75389,78839,85691,101411,102911

%N Sophie Germain primes in A154939.

%C 2*3+1=7, 5*2+1=11, ...

%t lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*(p+1)-p]&&PrimeQ[(p-1)*(p+1)+p],If[PrimeQ[p*2+1],AppendTo[lst,p]]],{n,8!}];lst

%t Select[Prime[Range[10000]],AllTrue[{2#+1,(#-1)(#+1)+#,(#-1)(#+1)-#},PrimeQ]&] (* _Harvey P. Dale_, Sep 21 2023 *)

%Y Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 17 2009