A038877 Primes p such that 6 is not a square mod p.

7, 11, 13, 17, 31, 37, 41, 59, 61, 79, 83, 89, 103, 107, 109, 113, 127, 131, 137, 151, 157, 179, 181, 199, 223, 227, 229, 233, 251, 257, 271, 277, 281, 347, 349, 353, 367, 373, 397, 401, 419, 421, 439, 443, 449

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Contribution from Cino Hilliard, Sep 06 2004: (Start)

Also primes p such that p divides 3^(p-1)/2 + 2^(p-1)/2.

Also primes p such that p divides 6^(p-1)/2 + 1.

Also primes p such that p divides 6^(p-1)/2 + 4^(p-1)/2. (End)

Inert rational primes in the field Q(sqrt(6)). - Alonso del Arte, Oct 14 2012

Primes congruent to 7, 11, 13, or 17 mod 24.

Examples

			17 is in the sequence because there is no solution to the equation x^2 - 6y = 17 in integers.
19 is NOT in the sequence because x^2 - 6y = 19 has solutions in integers, as does x^2 - 6y^2 = 19, e.g., x = 5, y = 1, and therefore (5 - sqrt(6))*(5 + sqrt(6)) = 19.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A003630.

Programs

Mathematica

Select[Prime@Range[120], JacobiSymbol[6, #] == -1 &] (* Vincenzo Librandi, Sep 08 2012 *)

PARI

forprime(p=2,500,if(kronecker(6,p)==-1, print1(p,", ")));
/* Joerg Arndt, Oct 15 2012 */

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Oct 15 2012

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Sep 08 2012