A162019 Double-safe primes which are also double-Sophie Germain primes.

11, 359, 719, 214559, 215399, 245639, 253679, 266999, 507359, 508559, 574439, 670919, 744599, 825479, 1017119, 1072199, 1184399, 1363679, 1621079, 1688279, 1786439, 2156039, 2377799, 2429279, 2633399, 2684999, 2900039, 3103799

Offset

1,1

Comments

The intersection of the primes in A066179 and those in A007700: they remain prime after each of two successive applications of the substitution p->(p-1)/2, and remain prime after each two successive applications of the substitution p->2p+1.

Links

Table of n, a(n) for n=1..28.

Formula

a(n) = 4*A023302(n) + 3 = (A157359(n)-3)/4. - R. J. Mathar, Jun 26 2009

Example

a(1)=11 is double safe: (11-1)/2=5; (5-1)/2=2, and double Sophie-Germain: 2*11+1=23; 2*23+1=47.

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[safe=(p-1)/2], If[PrimeQ[(safe-1)/2], If[PrimeQ[sophie=2*p+1], If[PrimeQ[2*sophie+1], AppendTo[lst, p]]]]], {n, 3*9!}]; lst

Crossrefs

Cf. A007700, A023302, A066179, A157359.

Sequence in context: A067428 A171630 A303116 * A066268 A257227 A176474

Adjacent sequences: A162016 A162017 A162018 * A162020 A162021 A162022

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 24 2009

Extensions

Edited by R. J. Mathar, Jun 26 2009

Status

approved