A097934 Primes p that divide 3^((p-1)/2) - 2^((p-1)/2).

5, 19, 23, 29, 43, 47, 53, 67, 71, 73, 97, 101, 139, 149, 163, 167, 173, 191, 193, 197, 211, 239, 241, 263, 269, 283, 293, 307, 311, 313, 317, 331, 337, 359, 379, 383, 389, 409, 431, 433, 457, 461, 479, 499, 503, 509, 523, 547, 557, 571, 577, 599, 601, 619

Offset: 1

Author

Cino Hilliard, Sep 04 2004

Keywords

• nonn
• easy

Comments

Rational primes that decompose in the field Q(sqrt(6)). - N. J. A. Sloane, Dec 26 2017

All terms belong to A038876(n) = Primes p such that 6 is a square mod p. Only first two terms of A038876(n), 2 and 3, do not belong to a(n). - Alexander Adamchuk, May 04 2007

From Jianing Song, Oct 13 2022: (Start)

Primes p such that kronecker(6,p) = 1 (or equivalently, kronecker(24,p) = 1).

Primes congruent to 1, 5, 9, 23 modulo 24. (End)

Examples

			For p=5, 3^2 - 2^2 = 5.
		

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. A038876 (primes p such that 6 is a square mod p), A038877 (rational primes that remain inert in the field Q(sqrt(6))).

Programs

Mathematica

okQ[n_]:=Module[{c=(n-1)/2},Divisible[3^c-2^c,n]]; Select[Prime[Range[200]],okQ]  (* Harvey P. Dale, Apr 13 2011 *)

PARI

/* Set x=3,d=1,s=-1 */
ptopm1d2(n,x,d,s) = { forprime(p=3,n,p2=(p-1)/2; y=x^p2 + s*(x-d)^p2; if(y%p==0,print1(p", "))) }

PARI

isA097934(p) == isprime(p) && kronecker(6,p) == 1 \\ Jianing Song, Oct 13 2022

Formula

a(n) = A038876(n+1). - Alexander Adamchuk, May 04 2007