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Search: id:A162019
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| A162019 |
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Double-safe primes which are also double-Sophie Germain primes. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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a(n)=4*A022302(n)+3 = (A157359(n)-3)/4. [R. J. Mathar, Jun 26 2009]
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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Sequence in context: A012220 A012138 A067428 this_sequence A066268 A000464 A024149
Adjacent sequences: A162016 A162017 A162018 this_sequence A162020 A162021 A162022
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 24 2009
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2009
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