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 A378184 #9 Jan 14 2025 09:49:28
%S A378184 8,4,12,8,4,20,20,28,16,12,4,8,4,24,36,8,16,20,16,76,36,4,24,16,56,8,
%T A378184 16,36,20,4,56,16,40,20,76,8,64,8,40,40,16,8,4,48,12,20,36,24,16,116,
%U A378184 76,4,24,20,20,100,100,84,56,52,64,16,8,4,24,12,44,56
%N A378184 With p(n) = A002144(n) = n-th Pythagorean prime, a(n) is the least k such p(n) + k is a Pythagorean prime and 2 p(n) + k + 1 is a non-Pythagorean prime; or a(n) = 0 if there is no such k.
%e A378184 5 + 8 = 13, the least Pythagorean prime after 5, and 5 + 13 + 1 = 19, a non-Pythagorean prime, so a(1) = 8.
%t A378184 s = Select[Prime[Range[450]], Mod[#, 4] == 1 &]
%t A378184 a[n_] := Select[Range[200], MemberQ[s, s[[n]] + #] && PrimeQ[2 s[[n]] + # + 1] &, 1]
%t A378184 Flatten[Table[a[n], {n, 1, 140}]]
%Y A378184 Cf., A000041, A002144, A002145.
%K A378184 nonn
%O A378184 1,1
%A A378184 _Clark Kimberling_, Jan 11 2025