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A059455
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Safe primes which are also Sophie Germain primes.
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34
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5, 11, 23, 83, 179, 359, 719, 1019, 1439, 2039, 2063, 2459, 2819, 2903, 2963, 3023, 3623, 3779, 3803, 3863, 4919, 5399, 5639, 6899, 6983, 7079, 7643, 7823, 10163, 10799, 10883, 11699, 12203, 12263, 12899, 14159, 14303, 14699, 15803, 17939
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes p such that both (p-1)/2 and 2*p+1 are prime.
Intersection of A005384 and A005385.
A156660(a(n))*A156659(a(n)) = 1; A156877 gives numbers of these numbers <= n. [From Reinhard Zumkeller, Feb 18 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
C. K. Caldwell, Cunningham Chains
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EXAMPLE
| 83 is a term because 2*83+1=167 and (83-1)/2=41 are both primes. Except for 5, all are congruent to 11 modulo 12. Primes "inside" Cunningham chains of first kind.
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MATHEMATICA
| lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)/2]&&PrimeQ[2*p+1], AppendTo[lst, p]], {n, 7!}]; lst [From Vladimir Orlovsky, Dec 02 2008]
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PROG
| (PARI) forprime(p=2, 1e5, if(isprime(p\2)&&isprime(2*p+1), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330.
Sequence in context: A024829 A097279 A106171 * A095030 A065114 A102171
Adjacent sequences: A059452 A059453 A059454 * A059456 A059457 A059458
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Feb 02 2001
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