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A162021 Triple-safe primes which are also triple-Sophie Germain primes. 0
8981279, 17313839, 18635759, 82062479, 82479119, 98517599, 112242479, 113164319, 152799359, 184829279, 193409039, 230749199, 296709839, 305598719, 339116159, 393280799, 406283519 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 05:04 EDT 2022. Contains 353826 sequences. (Running on oeis4.)