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 A164066 Number of partitions of n into Sophie Germain primes. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 3 12:59 EST 2022. Contains 358524 sequences. (Running on oeis4.)