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 A059455 Safe primes which are also Sophie Germain primes. 35
 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; text; internal format)
 OFFSET 1,1 COMMENTS Primes p such that both (p-1)/2 and 2*p+1 are prime. Intersection of A005384 and A005385. Except for 5, all are congruent to 11 modulo 12. Primes "inside" Cunningham chains of first kind. A156660(a(n))*A156659(a(n)) = 1; A156877 gives numbers of these numbers <= n. - Reinhard Zumkeller, Feb 18 2009 Infinite under Dickson's conjecture. - Charles R Greathouse IV, Jul 18 2012 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 C. K. Caldwell, Cunningham Chains EXAMPLE 83 is a term because 2*83+1=167 and (83-1)/2=41 are both primes. MATHEMATICA lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)/2]&&PrimeQ[2*p+1], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 02 2008 *) Select[Prime[Range[1000]], AllTrue[{(# - 1)/2, 2 # + 1}, PrimeQ] &] (* requires Mathematica 10+; Feras Awad, Dec 19 2018 *) PROG (PARI) forprime(p=2, 1e5, if(isprime(p\2)&&isprime(2*p+1), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011 (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))) A059455_list = list(islice(A059455_gen(), 10)) # Chai Wah Wu, Jul 12 2022 CROSSREFS Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330, A156659, A156660, A156877, A162019. Sequence in context: A097279 A106171 A276174 * A095030 A065114 A309730 Adjacent sequences: A059452 A059453 A059454 * A059456 A059457 A059458 KEYWORD nonn AUTHOR Labos Elemer, Feb 02 2001 STATUS approved

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Last modified June 3 15:36 EDT 2023. Contains 363116 sequences. (Running on oeis4.)