|
%I #10 Dec 17 2021 08:58:28
%S 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,
%T 33,35,39,42,46,50,54,58,63,68,73,79,85,90,98,105,112,121,128,137,147,
%U 156,167,178,189,201,215,228,242,258,272,289,307,324,344,364,383,407,429
%N Number of partitions of n into Sophie Germain primes.
%H Andrew Howroyd, <a href="/A164066/b164066.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A005384(k)). - _Andrew Howroyd_, Dec 28 2017
%e e(10) = #{5+5,5+3+2,3+3+2+2,2+2+2+2+2} = 4;
%e e(11) = #{11,5+3+3,5+2+2+2,3+3+3+2,3+2+2+2+2} = 5.
%t terms = 1000;
%t sgprimes = Select[Prime[Range[terms]], PrimeQ[2# + 1]&];
%t CoefficientList[Times @@ (1/(1 - x^sgprimes) + O[x]^(terms+1)), x] // Rest (* _Jean-François Alcover_, Dec 17 2021 *)
%o (PARI)
%o ok(n)={isprime(n) && isprime(2*n+1)}
%o {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
%Y Cf. A164067, A000607, A000041, A005384.
%K nonn
%O 1,5
%A _Reinhard Zumkeller_, Aug 09 2009
|
