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 A335045 #12 Jul 14 2020 23:47:23
%S A335045 0,3,3,5,7,3,5,7,3,5,7,23,11,13,3,5,7,0,11,13,3,5,7,47,11,13,53,17,19,
%T A335045 3,5,7,0,11,13,3,5,7,0,11,13,83,17,19,89,23,37,0,29,31,3,5,7,3,5,7,
%U A335045 113,11,13,0,17,19,0,23,31,131,29,31,3,5,7,0,11,13,3,5,7,0,11,13,0,17,19,167,23,37,173
%N A335045 Minimal common prime of two Goldbach partitions of 2n and 2(n+1) or zero if no common prime exists.
%C A335045 a(n) is the least prime p such that 2n-p is in A001359, or 0 if no such p exists. - _Robert Israel_, May 21 2020
%H A335045 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A335045 4 = 2+2 and 6 = 3+3. Since those are the only available Goldbach partitions and they have no common prime, a(4/2) = a(2) = 0.
%e A335045 14 = 3+11 and 16 = 3+13, so a(14/2) = a(7) = 3.
%p A335045 N:= 100:
%p A335045 P:= select(isprime, {seq(i,i=3..2*N-1,2)}):
%p A335045 T:= P intersect map(`-`,P,2):
%p A335045 f:= n -> subs(infinity=0, min(P intersect map(t -> 2*n-t, T))):
%p A335045 map(f, [$2..N]); # _Robert Israel_, May 21 2020
%t A335045 d[n_]:=Flatten[Cases[FrobeniusSolve[{1,1},2*n],{__?PrimeQ}]]
%t A335045 e[n_]:=Intersection[d[n],d[n+1]]; f[n_]:=If[e[n]=={},0,Min[e[n]]];f/@Range[2,100]
%Y A335045 Cf. A001359, A002372, A002373, A002375, A045917, A335046.
%K A335045 nonn
%O A335045 2,2
%A A335045 _Ivan N. Ianakiev_, May 21 2020