A164066 Number of partitions of n into Sophie Germain primes.

0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 20, 23, 25, 27, 30, 33, 35, 39, 42, 46, 50, 54, 58, 63, 68, 73, 79, 85, 90, 98, 105, 112, 121, 128, 137, 147, 156, 167, 178, 189, 201, 215, 228, 242, 258, 272, 289, 307, 324, 344, 364, 383, 407, 429

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

G.f.: Product_{k>=1} 1/(1 - x^A005384(k)). - Andrew Howroyd, Dec 28 2017

Example

e(10) = #{5+5,5+3+2,3+3+2+2,2+2+2+2+2} = 4;
e(11) = #{11,5+3+3,5+2+2+2,3+3+3+2,3+2+2+2+2} = 5.

Mathematica

terms = 1000;
sgprimes = Select[Prime[Range[terms]], PrimeQ[2# + 1]&];
CoefficientList[Times @@ (1/(1 - x^sgprimes) + O[x]^(terms+1)), x] // Rest (* Jean-François Alcover, Dec 17 2021 *)

Prog

(PARI)
ok(n)={isprime(n) && isprime(2*n+1)}
{my(n=80); Vec(prod(k=1, n, if(ok(k), 1/(1-x^k) + O(x*x^n), 1))-1, -n)} \\ Andrew Howroyd, Dec 28 2017

Crossrefs

Cf. A164067, A000607, A000041, A005384.

Sequence in context: A008625 A029148 A067842 * A053251 A090184 A174575

Adjacent sequences: A164063 A164064 A164065 * A164067 A164068 A164069

Keyword

nonn

Author

Reinhard Zumkeller, Aug 09 2009

Status

approved