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 A366193 #9 Oct 06 2023 10:59:55 %S A366193 1,0,0,0,1,0,9,0,0,6,0,6,0,0,3,15,1,2,0,1,0,6,1,2,6,3,9,0,0,6,15,4,5, %T A366193 0,3,2,6,0,2,3,1,9,0,4,3,0,7,0,3,1,6,6,1,5,6,0,2,6,0,6,0,1,0,0,13,0,6, %U A366193 0,6,3,4,11,12,0,3,0,9,3,0,3,0,21,9,2,3,0,6,18,0,3 %N A366193 For n >= 0, a(n) is the least x >= 0 such that x^2 + (x + 2*n)^2 + 1 = p, p prime number (A000040). %C A366193 For a(n) = 0 the resulting primes p >= 5 see in A002496. %H A366193 Stoyan I. Dimitrov, <a href="https://arxiv.org/abs/2011.03967">A ternary diophantine inequality by primes with one of the form p = x^2 + y^2 + 1</a>, arXiv:2011.03967 [math.NT], 2020. %F A366193 a(n) = 0 for n from A001912. %e A366193 n = 0: x^2 + x^2 + 1 = p is valid for the least x = 1, p = 3, thus a(0) = 1. %e A366193 n = 6: x^2 + (x + 12)^2 + 1 = p is valid for the least x = 9, p = 523, thus a(6) = 9. %o A366193 (PARI) a(n) = my(x=0); while (!isprime(x^2 + (x + 2*n)^2 + 1), x++); x; \\ _Michel Marcus_, Oct 03 2023 %Y A366193 Cf. A000040, A001912, A002496. %K A366193 nonn %O A366193 0,7 %A A366193 _Ctibor O. Zizka_, Oct 03 2023 %E A366193 More terms from _Michel Marcus_, Oct 03 2023