A293859 Prime factors of numbers of the form k^2 + 10.

2, 5, 7, 11, 13, 19, 23, 37, 41, 47, 53, 59, 89, 103, 127, 131, 139, 157, 167, 173, 179, 197, 211, 223, 241, 251, 263, 277, 281, 293, 317, 331, 367, 373, 379, 383, 397, 401, 409, 419, 449, 463, 487, 491, 499, 503, 521, 557, 569, 571, 601, 607, 613, 619, 641

Offset: 1

Author

J. Lowell, Oct 17 2017

Keywords

• nonn

Comments

Primes p such that Legendre(-10,p) = 0 or 1. - N. J. A. Sloane, Dec 26 2017

Question: Is there a comment of the form "a prime number is in this sequence if and only if it is congruent to (list of appropriate values) mod n" for this sequence?

From Robert Israel, Nov 19 2017: (Start)

Prime p > 5 is in the sequence iff -10 is a quadratic residue mod p.

Thus p is either in the intersection of A002144 and A038879 or in neither of them.

Primes == 1, 2, 5, 7, 9, 11, 13, 19, 23, or 37 (mod 40). (End)

Examples

			7 is in the sequence because 2^2 + 10 = 14 is 2 times 7.
19 is in the sequence because 3^2 + 10 = 19.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A038879, A114948.

Programs

Maple

select(isprime, [seq(seq(i*40+j, j = [1, 2, 5, 7, 9, 11, 13, 19, 23, 37]), i=0..40)]); # Robert Israel, Nov 19 2017
# Load the Maple program HH given in A296920. Then run HH(-10, 200); This produces A155488, A296925, A293859. - N. J. A. Sloane, Dec 26 2017

Mathematica

Select[Prime@ Range@ 120, {} != FindInstance[# x == n^2 + 10 && n >= 0 && x > 0, {n, x}, Integers, 1] &] (* Giovanni Resta, Oct 19 2017 *)

Extensions

More terms from Giovanni Resta, Oct 19 2017