cp's OEIS Frontend

A211397 Number of Sophie Germain primes less than 2^n.

%I A211397 #35 Jul 25 2025 09:00:17
%S A211397 0,2,3,4,6,8,11,18,26,39,62,103,170,281,474,834,1464,2555,4493,8051,
%T A211397 14499,26375,48024,88175,161833,297544,549330,1018008,1893255,3527324,
%U A211397 6588118,12334363,23140567,43497488,81930886,154587025,292149120,552997218,1048340476,1990145943,3783145017
%N A211397 Number of Sophie Germain primes less than 2^n.
%H A211397 Paul D. Beale, <a href="http://arxiv.org/abs/1411.2484">A new class of scalable parallel pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers</a>, arXiv preprint arXiv:1411.2484 [physics.comp-ph], 2014-2015.
%H A211397 Jetanat Datephanyawat and Paul D. Beale, <a href="https://arxiv.org/abs/1811.11629">Class of scalable parallel and vectorizable pseudorandom number generators based on non-cryptographic RSA exponentiation ciphers</a>, arXiv:1811.11629 [cs.CR], 2018-2021.
%t A211397 nmax = 37; stable = Table[0, {nmax}];
%t A211397 Do[s = 0;
%t A211397   Do[If[And[PrimeQ[i], PrimeQ[2 i + 1]], s++], {i, 1, 2^n - 1}];
%t A211397   Print[n, " ", s]; stable[[n]] = s, {n, 1, nmax}];
%t A211397 stable (* _Paul D. Beale_, Sep 19 2014 *)
%o A211397 (PARI) a211397(n) = {local(r,i); r=0; for(i=1, 2^n-1, if(isprime(i)&&isprime(2*i+1), r=r+1)); r}
%Y A211397 Cf. A211395, A005385.
%K A211397 nonn
%O A211397 1,2
%A A211397 _Michael B. Porter_, Feb 08 2013
%E A211397 a(30)-a(37) from _Paul D. Beale_, Sep 19 2014
%E A211397 a(38)-a(41) from _Amiram Eldar_, Jul 25 2025