A366193 - OEIS

%I #9 Oct 06 2023 10:59:55

%S 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 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 0,6,3,4,11,12,0,3,0,9,3,0,3,0,21,9,2,3,0,6,18,0,3

%N 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 For a(n) = 0 the resulting primes p >= 5 see in A002496.

%H 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 a(n) = 0 for n from A001912.

%e n = 0: x^2 + x^2 + 1 = p is valid for the least x = 1, p = 3, thus a(0) = 1.

%e n = 6: x^2 + (x + 12)^2 + 1 = p is valid for the least x = 9, p = 523, thus a(6) = 9.

%o (PARI) a(n) = my(x=0); while (!isprime(x^2 + (x + 2*n)^2 + 1), x++); x; \\ _Michel Marcus_, Oct 03 2023

%Y Cf. A000040, A001912, A002496.

%K nonn

%O 0,7

%A _Ctibor O. Zizka_, Oct 03 2023

%E More terms from _Michel Marcus_, Oct 03 2023