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).

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

Offset

0,7

Comments

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

Links

Table of n, a(n) for n=0..89.

Stoyan I. Dimitrov, A ternary diophantine inequality by primes with one of the form p = x^2 + y^2 + 1, arXiv:2011.03967 [math.NT], 2020.

Formula

a(n) = 0 for n from A001912.

Example

n = 0: x^2 + x^2 + 1 = p is valid for the least x = 1, p = 3, thus a(0) = 1.
n = 6: x^2 + (x + 12)^2 + 1 = p is valid for the least x = 9, p = 523, thus a(6) = 9.

Prog

(PARI) a(n) = my(x=0); while (!isprime(x^2 + (x + 2*n)^2 + 1), x++); x; \\ Michel Marcus, Oct 03 2023

Crossrefs

Cf. A000040, A001912, A002496.

Sequence in context: A254968 A019940 A257435 * A296458 A199870 A132267

Adjacent sequences: A366190 A366191 A366192 * A366194 A366195 A366196

Keyword

nonn

Author

Ctibor O. Zizka, Oct 03 2023

Extensions

More terms from Michel Marcus, Oct 03 2023

Status

approved