OFFSET
0,5
COMMENTS
To be precise, the number of Sophie Germain primes p, 2^n < p <= 2^(n+1). Since 2 is a Sophie Germain prime, this precise definition is important only for determining a(0) and a(1). The alternative definition (with 2^n <= p < 2^(n+1)) would give the sequence 0, 2, 1, 1, 2, 2, 3, 7, 8, 13, 23, 41, 67, 111, 193, ...
LINKS
Paul D. Beale, A new class of scalable parallel pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers, arXiv preprint arXiv:1411.2484, 2014-2015.
Paul D. Beale, Jetanat Datephanyawat, Class of scalable parallel and vectorizable pseudorandom number generators based on non-cryptographic RSA exponentiation ciphers, arXiv:1811.11629 [cs.CR], 2018.
FORMULA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Brad Clardy, Feb 08 2013
EXTENSIONS
a(29)-a(36) from Paul D. Beale, Sep 19 2014
STATUS
approved