A211395 Number of Sophie Germain primes between 2^n and 2^(n+1).
1, 1, 1, 1, 2, 2, 3, 7, 8, 13, 23, 41, 67, 111, 193, 360, 630, 1091, 1938, 3558, 6448, 11876, 21649, 40151, 73658, 135711, 251786, 468678, 875247, 1634069, 3060794, 5746245, 10806204, 20356921, 38433398, 72656139, 137562095, 260848098, 495343258, 941805467, 1792999074
Offset: 0
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 = 36; rtable = Table[0, {nmax}]; Do[r = 0; Do[If[And[PrimeQ[i], PrimeQ[2 i + 1]], r++], {i, 1 + 2^n, 2^(n + 1)}]; Print[n, " ", r]; rtable[[n + 1]] = r, {n, 0, nmax - 1}]; rtable (* Paul D. Beale, Sep 19 2014 *) -
PARI
a211395(n) = {local(r,i); r=0; for(i=2^n+1, 2^(n+1), if(isprime(i)&&isprime(2*i+1), r=r+1)); r} \\ Michael B. Porter, Feb 08 2013
Formula
Extensions
a(29)-a(36) from Paul D. Beale, Sep 19 2014
a(37)-a(40) from Amiram Eldar, Jul 25 2025
Comments