This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299197 #5 Feb 16 2025 08:33:53
%S A299197 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 A299197 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 A299197 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 A299197 Number of partitions of n into distinct parts that are greater of twin primes (A006512).
%H A299197 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%H A299197 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A299197 G.f.: Product_{k>=1} (1 + x^A006512(k)).
%e A299197 a(31) = 2 because we have [31] and [19, 7, 5].
%t A299197 nmax = 105; CoefficientList[Series[Product[1 + Boole[PrimeQ[k] && PrimeQ[k - 2]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y A299197 Cf. A000586, A000607, A001097, A006512, A077608, A129363, A283875, A283876, A299196.
%K A299197 nonn
%O A299197 0,32
%A A299197 _Ilya Gutkovskiy_, Feb 04 2018