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

2, 13, 19, 43, 47, 53, 59, 67, 83, 89, 101, 103, 127, 137, 149, 151, 157, 179, 191, 223, 229, 239, 251, 257, 263, 271, 281, 293, 307, 331, 349, 353, 359, 373, 383, 389, 409, 421, 433, 443, 457, 461, 463, 467, 491, 509, 523, 557, 563, 569, 577, 587, 593, 599

Offset: 1

Author

N. J. A. Sloane, Dec 26 2017

Keywords

• nonn
• easy

Comments

From Jianing Song, Apr 21 2022: (Start)

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.

Primes p such that p^8 == 1 (mod 17).

Primes p == 1, 2, 4, 8, 9, 13, 15, 16 (mod 17). (End)

Links

• Jianing Song, Table of n, a(n) for n = 1..10000
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A011584 (kronecker symbol modulo 17).

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).

Cf. A038890 (inert rational primes in the field Q(sqrt(17))).

Programs

Magma

[p: p in PrimesUpTo(600) | KroneckerSymbol(p, 17) eq 1]; // Vincenzo Librandi, Apr 09 2020

Maple

Load the Maple program HH given in A296920. Then run HH(17, 200); This produces A296938, A038890, A038889.

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#, 17]==1&] (* Vincenzo Librandi, Apr 09 2020 *)

PARI

isA296938(p) = isprime(p) && kronecker(p,17) == 1 \\ Jianing Song, Apr 21 2022