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

1,1

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].

Links

Table of n, a(n) for n=1..17.

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

Crossrefs

Sequence in context: A251157 A337963 A234192 * A157815 A157821 A106787

Adjacent sequences: A162018 A162019 A162020 * A162022 A162023 A162024

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 25 2009

Extensions

Edited by R. J. Mathar, Jun 26 2009

Status

approved