A211397 Number of Sophie Germain primes less than 2^n.
0, 2, 3, 4, 6, 8, 11, 18, 26, 39, 62, 103, 170, 281, 474, 834, 1464, 2555, 4493, 8051, 14499, 26375, 48024, 88175, 161833, 297544, 549330, 1018008, 1893255, 3527324, 6588118, 12334363, 23140567, 43497488, 81930886, 154587025, 292149120, 552997218, 1048340476, 1990145943, 3783145017
Offset: 1
Keywords
Links
- Paul D. Beale, A new class of scalable parallel pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers, arXiv preprint arXiv:1411.2484 [physics.comp-ph], 2014-2015.
- Jetanat Datephanyawat and Paul D. Beale, Class of scalable parallel and vectorizable pseudorandom number generators based on non-cryptographic RSA exponentiation ciphers, arXiv:1811.11629 [cs.CR], 2018-2021.
Programs
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Mathematica
nmax = 37; stable = Table[0, {nmax}]; Do[s = 0; Do[If[And[PrimeQ[i], PrimeQ[2 i + 1]], s++], {i, 1, 2^n - 1}]; Print[n, " ", s]; stable[[n]] = s, {n, 1, nmax}]; stable (* Paul D. Beale, Sep 19 2014 *) -
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}
Extensions
a(30)-a(37) from Paul D. Beale, Sep 19 2014
a(38)-a(41) from Amiram Eldar, Jul 25 2025