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A162019 Double-safe primes which are also double-Sophie Germain primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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*A022302(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

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

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Last modified October 31 19:00 EDT 2020. Contains 338111 sequences. (Running on oeis4.)