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

Author

Vladimir Joseph Stephan Orlovsky, Jun 24 2009

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A007700, A023302, A066179, A157359.

Programs

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

Formula

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

Extensions

Edited by R. J. Mathar, Jun 26 2009