cp's OEIS Frontend

A296938 Rational primes that decompose in the field Q(sqrt(17)).

%I A296938 #21 Sep 08 2022 08:46:20
%S A296938 2,13,19,43,47,53,59,67,83,89,101,103,127,137,149,151,157,179,191,223,
%T A296938 229,239,251,257,263,271,281,293,307,331,349,353,359,373,383,389,409,
%U A296938 421,433,443,457,461,463,467,491,509,523,557,563,569,577,587,593,599
%N A296938 Rational primes that decompose in the field Q(sqrt(17)).
%C A296938 From _Jianing Song_, Apr 21 2022: (Start)
%C A296938 Primes p such that kronecker(17, p) = kronecker(p, 17) = 1, where kronecker() is the kronecker symbol. That is to say, primes p that are quadratic residues modulo 17.
%C A296938 Primes p such that p^8 == 1 (mod 17).
%C A296938 Primes p == 1, 2, 4, 8, 9, 13, 15, 16 (mod 17). (End)
%H A296938 Jianing Song, <a href="/A296938/b296938.txt">Table of n, a(n) for n = 1..10000</a>
%H A296938 <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%p A296938 Load the Maple program HH given in A296920. Then run HH(17, 200); This produces A296938, A038890, A038889.
%t A296938 Select[Prime[Range[200]], JacobiSymbol[#, 17]==1&] (* _Vincenzo Librandi_, Apr 09 2020 *)
%o A296938 (Magma) [p: p in PrimesUpTo(600) | KroneckerSymbol(p, 17) eq 1]; // _Vincenzo Librandi_, Apr 09 2020
%o A296938 (PARI) isA296938(p) = isprime(p) && kronecker(p,17) == 1 \\ _Jianing Song_, Apr 21 2022
%Y A296938 Cf. A011584 (kronecker symbol modulo 17).
%Y A296938 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), A296937 (D=13), this sequence (D=17).
%Y A296938 Cf. A038890 (inert rational primes in the field Q(sqrt(17))).
%K A296938 nonn,easy
%O A296938 1,1
%A A296938 _N. J. A. Sloane_, Dec 26 2017