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 A235645 #9 Feb 16 2025 08:33:21
%S A235645 0,1,1,1,2,1,2,2,2,2,3,3,3,2,3,3,5,4,3,3,4,5,5,5,5,5,5,4,6,6,5,6,6,4,
%T A235645 6,7,8,8,8,7,9,8,8,7,9,8,9,8,6,9,9,10,10,9,9,12,12,11,13,12,10,11,11,
%U A235645 9,12,11,12,11,11,12,15,14,12,12,12
%N A235645 From Goldbach's conjecture and Chen's theorem: number of decompositions of 2n as the sum of either two primes, or a prime and a semiprime.
%C A235645 The first 15 terms from this sequence and from A045917 are identical.
%H A235645 Jean-François Alcover, <a href="/A235645/b235645.txt">Table of n, a(n) for n = 1..10000</a>
%H A235645 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/ChensTheorem.html">Chen's theorem</a>
%H A235645 Wikipedia, <a href="http://en.wikipedia.org/wiki/Chen's_theorem">Chen's theorem</a>
%e A235645 40 = 23+17 = 29+11 = 37+3, so a(20) = 3.
%e A235645 Compare with 40 = 23+17 = 29+11 = 31+9 = 37+3 and A045917(20) = 4.
%t A235645 a[n_] := Count[IntegerPartitions[2*n, {2}], {p_, q_} /; PrimeQ[p] && (PrimeQ[q] || Length[FactorInteger[q]] == 2)]; Table[a[n], {n, 1, 100}]
%Y A235645 Cf. A002375, A045917.
%K A235645 nonn
%O A235645 1,5
%A A235645 _Jean-François Alcover_, Jan 13 2014