|
%I #30 Oct 13 2022 13:56:59
%S 5,19,23,29,43,47,53,67,71,73,97,101,139,149,163,167,173,191,193,197,
%T 211,239,241,263,269,283,293,307,311,313,317,331,337,359,379,383,389,
%U 409,431,433,457,461,479,499,503,509,523,547,557,571,577,599,601,619
%N Primes p that divide 3^((p-1)/2) - 2^((p-1)/2).
%C Rational primes that decompose in the field Q(sqrt(6)). - _N. J. A. Sloane_, Dec 26 2017
%C 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
%C From _Jianing Song_, Oct 13 2022: (Start)
%C Primes p such that kronecker(6,p) = 1 (or equivalently, kronecker(24,p) = 1).
%C Primes congruent to 1, 5, 9, 23 modulo 24. (End)
%H Vincenzo Librandi, <a href="/A097934/b097934.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%F a(n) = A038876(n+1). - _Alexander Adamchuk_, May 04 2007
%e For p=5, 3^2 - 2^2 = 5.
%t okQ[n_]:=Module[{c=(n-1)/2},Divisible[3^c-2^c,n]]; Select[Prime[Range[200]],okQ] (* _Harvey P. Dale_, Apr 13 2011 *)
%o (PARI) /* Set x=3,d=1,s=-1 */
%o 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", "))) }
%o (PARI) isA097934(p) == isprime(p) && kronecker(6,p) == 1 \\ _Jianing Song_, Oct 13 2022
%Y Cf. A038876 (primes p such that 6 is a square mod p), A038877 (rational primes that remain inert in the field Q(sqrt(6))).
%K nonn,easy
%O 1,1
%A _Cino Hilliard_, Sep 04 2004
|
