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

1,1

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A003630.

Sequence in context: A038931 A141189 A191035 * A019351 A032666 A237183

Adjacent sequences: A038874 A038875 A038876 * A038878 A038879 A038880

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved