A162021 Triple-safe primes which are also triple-Sophie Germain primes.

8981279, 17313839, 18635759, 82062479, 82479119, 98517599, 112242479, 113164319, 152799359, 184829279, 193409039, 230749199, 296709839, 305598719, 339116159, 393280799, 406283519

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 25 2009

Keywords

• nonn

Comments

The intersection of the primes in A157358 and those in A023272: they remain prime after each

of three successive applications of the substitution p->(p-1)/2, and remain prime after each

three successive applications of the substitution p->2p+1. Therefore the sequence is a subsequence

of A162019.

They appear for example in the middle of chains started in A059767 or in even longer Cunningham chains. [R. J. Mathar, Jun 26 2009].

Programs

Mathematica

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

Extensions

Edited by R. J. Mathar, Jun 26 2009