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

1,1

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

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 *)

Prog

(Magma) [p: p in PrimesUpTo(600) | KroneckerSymbol(p, 17) eq 1]; // Vincenzo Librandi, Apr 09 2020
(PARI) isA296938(p) = isprime(p) && kronecker(p, 17) == 1 \\ Jianing Song, Apr 21 2022

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))).

Sequence in context: A298051 A298656 A027705 * A350976 A296199 A121181

Adjacent sequences: A296935 A296936 A296937 * A296939 A296940 A296941

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 26 2017

Status

approved