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 A188766 #12 Feb 28 2020 03:32:35
%S A188766 1,12,15,17,18,22,23,24,25,27,29,31,33,37,42,44,45,46,49,50,51,52,53,
%T A188766 54,58,59,60,61,63,64,66,67,69,70,71,73,77,79,80,81,82,83,84,85,86,87,
%U A188766 90,92,95,96,97,98,99,100,101,102,107,110,112,115,117,118,119
%N A188766 Numbers n such that the number of decompositions of 2n into sum of two primes (counting 1 as a prime) is 1 or a composite.
%C A188766 Arises in Goldbach conjecture.
%F A188766 {integers n > 0 such that A001031(n) is in A018252} = {integers n > 0 such that A001031(n) is not in A000040}.
%e A188766 1 is a term because there is a unique decomposition of 2*1 = 2 into a sum of two primes (counting 1 as a prime), namely 2 = 1 + 1.
%e A188766 12 is a term because there are 4 decompositions of 2*12 = 24 into a sum of two primes (counting 1 as a prime), namely 1 + 23, 5 + 19, 7 + 17, and 11 + 13, and 4 is a composite number.
%o A188766 (Sage)
%o A188766 def is_A188766(n):
%o A188766 pp = set(prime_range(2*n+1)+[1])
%o A188766 return not is_prime(len([x for x in Partitions(2*n,length=2) if set(x) <= pp]))
%o A188766 # _D. S. McNeil_, Apr 10 2011
%Y A188766 Cf. A000040, A001031, A002808, A018252.
%K A188766 nonn,easy
%O A188766 1,2
%A A188766 _Jonathan Vos Post_, Apr 09 2011