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A038877 Primes p such that 6 is not a square mod p. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 28 19:21 EDT 2020. Contains 338064 sequences. (Running on oeis4.)