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 A255472 #25 Oct 23 2017 13:10:06
%S A255472 0,0,0,1,2,1,2,2,2,2,2,3,3,2,3,1,4,4,1,3,4,3,3,4,4,3,5,3,3,6,1,5,6,2,
%T A255472 5,5,4,5,6,4,4,8,4,3,8,3,5,7,2,5,7,5,6,6,6,6,9,5,4,12,3,5,10,2,5,7,6,
%U A255472 5,6,6,5,11,5,4,11,2,8,8,3,7,10,5,4,9,8,5
%N A255472 Number of decompositions of 2n into sums of two primes p <= q such that one or both p and q are elements of A023201.
%C A255472 Conjecture: for all n > 3, a(n) > 0.
%C A255472 If 2n = p + q and p+6 is also a prime, 2n+6 can be written as the sum of two primes p+6 and q.
%C A255472 The conjecture is weaker than a conjecture of Sun posed in 2012 (see A219055). - _Zhi-Wei Sun_, Mar 18 2015
%H A255472 Lei Zhou, <a href="/A255472/b255472.txt">Table of n, a(n) for n = 1..10000</a>
%H A255472 Lei Zhou, <a href="/A255472/a255472.jpg">Plot</a> for 0<n<=200000.
%H A255472 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A255472 n=4: 2n=8=3+5, 5+6=11 is also a prime number. This is the only occurrence, so a(4)=1.
%e A255472 n=5: 2n=10=3+7=5+5. Both 5+6=11 and 7+6=13 are prime numbers. Two occurrences found, so a(5)=2.
%t A255472 Table[e = 2 n; ct = 0; p1 = 2; While[p1 = NextPrime[p1]; p1 <= n, p2 = e - p1; If[PrimeQ[p2], If[PrimeQ[p1 + 6] || PrimeQ[p2 + 6], ct++]]]; ct, {n, 1, 100}]
%o A255472 (PARI) a(n) = {nb = 0; forprime(p=2, 2*n, if ((q=2*n-p) && (q <= p) && isprime(q=2*n-p) && (isprime(q+6) || isprime(p+6)), nb++);); nb;} \\ _Michel Marcus_, Mar 01 2015
%Y A255472 Cf. A023201, A045917, A199920, A219055.
%K A255472 nonn,easy
%O A255472 1,5
%A A255472 _Lei Zhou_, Feb 23 2015