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 A240714 #13 May 01 2014 05:18:16
%S A240714 2,4,6,8,10,12,14,16,18,20,32,68,152,458
%N A240714 Even numbers whose unordered two primes decomposition set does not contain two groups of n = p1+p2 = p3+p4 such that |p1-p3| = 6 or 12.
%C A240714 p1=p2 or p3=p4 allowed.
%C A240714 Conjecture: this sequence is finite and all elements are listed.
%e A240714 For number 152, 152 = 3+149 = 13+139 = 43+109 = 73+79. The differences of adjacent smaller primes in each of the decomposition groups are 10, 30, 30 respectively. None of them is 6 or 12. So 152 is included.
%t A240714 n = 0; Table[
%t A240714 While[n++; s = 2*n; ct = 0; p = 1;
%t A240714 While[p = NextPrime[p]; p <= n,
%t A240714 If[PrimeQ[s - p], ok = 0; a1 = p - 12; b1 = s - a1; a2 = p - 6;
%t A240714 b2 = s - a2; a3 = p + 6; b3 = s - a3; a4 = p + 12; b4 = s - a4;
%t A240714 If[a1 > 0, If[PrimeQ[a1] && PrimeQ[b1], ok = 1]];
%t A240714 If[a2 > 0, If[PrimeQ[a2] && PrimeQ[b2], ok = 1]];
%t A240714 If[a3 <= n, If[PrimeQ[a3] && PrimeQ[b3], ok = 1]];
%t A240714 If[a4 <= n, If[PrimeQ[a4] && PrimeQ[b4], ok = 1]];
%t A240714 If[ok == 1, ct++]]]; ct != 0]; s, {k, 1, 14}]
%Y A240714 Cf. A240713.
%K A240714 nonn,fini
%O A240714 1,1
%A A240714 _Lei Zhou_, Apr 10 2014