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%I #20 Apr 21 2022 21:56:21
%S 3,17,23,29,43,53,61,79,101,103,107,113,127,131,139,157,173,179,181,
%T 191,199,211,233,251,257,263,269,277,283,311,313,337,347,367,373,389,
%U 419,433,439,443,467,491,503,521,523,547,563,569,571,599,601,607,641
%N Rational primes that decompose in the field Q(sqrt(13)).
%C Is this the same sequence as A141188 or A038883? - _R. J. Mathar_, Jan 02 2018
%C From _Jianing Song_, Apr 21 2022: (Start)
%C Primes p such that Kronecker(13, p) = Kronecker(p, 13) = 1, where Kronecker() is the Kronecker symbol. That is to say, primes p that are quadratic residues modulo 13.
%C Primes p such that p^6 == 1 (mod 13).
%C Primes p == 1, 3, 4, 9, 10, 12 (mod 13). (End)
%H Jianing Song, <a href="/A296937/b296937.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%F Equals A038883 \ {13}. - _Jianing Song_, Apr 21 2022
%p Load the Maple program HH given in A296920. Then run HH(13, 200); This produces A296937, A038884, A038883.
%o (PARI) isA296937(p) = isprime(p) && kronecker(p,13) == 1 \\ _Jianing Song_, Apr 21 2022
%Y Cf. A011583 (kronecker symbol modulo 13), A038883.
%Y Rational primes that decompose in the quadratic field with discriminant D: A139513 (D=-20), A191019 (D=-19), A191018 (D=-15), A296920 (D=-11), A033200 (D=-8), A045386 (D=-7), A002144 (D=-4), A002476 (D=-3), A045468 (D=5), A001132 (D=8), A097933 (D=12), this sequence (D=13), A296938 (D=17).
%Y Cf. A038884 (inert rational primes in the field Q(sqrt(13))).
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Dec 26 2017
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