A299197 - OEIS

%I #4 Feb 04 2018 17:29:29

%S 1,0,0,0,0,1,0,1,0,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,2,1,0,

%T 0,0,1,1,1,1,0,0,0,2,2,0,0,0,1,1,2,1,0,0,0,2,2,1,0,0,0,2,2,2,0,0,1,1,

%U 3,1,1,0,0,2,3,2,0,0,1,2,3,2,1,0,0,2,3,3,0,0,0,1,4,3,1,0,0,2,3,3,2,0,0,1,4,4

%N Number of partitions of n into distinct parts that are greater of twin primes (A006512).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} (1 + x^A006512(k)).

%e a(31) = 2 because we have [31] and [19, 7, 5].

%t nmax = 105; CoefficientList[Series[Product[1 + Boole[PrimeQ[k] && PrimeQ[k - 2]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000586, A000607, A001097, A006512, A077608, A129363, A283875, A283876, A299196.

%K nonn

%O 0,32

%A _Ilya Gutkovskiy_, Feb 04 2018