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A059455
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Safe primes which are also Sophie Germain primes.
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37
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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
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OFFSET
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1,1
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COMMENTS
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Primes p such that both (p-1)/2 and 2*p+1 are prime.
Except for 5, all are congruent to 11 modulo 12.
Primes "inside" Cunningham chains of first kind.
See A162019 for the subset of a(n) that are "reproduced" by the application of the transformations (a(n)-1)/2 and 2*a(n)+1 to the set a(n). - Richard R. Forberg, Mar 05 2015
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LINKS
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EXAMPLE
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83 is a term because 2*83+1=167 and (83-1)/2=41 are both primes.
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MATHEMATICA
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Select[Prime[Range[1000]], AllTrue[{(# - 1)/2, 2 # + 1}, PrimeQ] &] (* requires Mathematica 10+; Feras Awad, Dec 19 2018 *)
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PROG
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(Magma) [p: p in PrimesUpTo(20000) |IsPrime((p-1) div 2) and IsPrime(2*p+1)]; // Vincenzo Librandi, Oct 31 2014
(Python)
from itertools import count, islice
from sympy import isprime, prime
def A059455_gen(): # generator of terms
return filter(lambda p:isprime(p>>1) and isprime(p<<1|1), (prime(i) for i in count(1)))
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CROSSREFS
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Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330, A156659, A156660, A156877, A162019.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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