A296921 Rational primes that decompose in the field Q(sqrt(-163)).

41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 167, 173, 179, 197, 199, 223, 227, 251, 263, 281, 307, 313, 347, 359, 367, 373, 379, 383, 397, 409, 419, 421, 439, 457, 461, 487, 499, 503, 523, 547, 563, 577, 593, 607, 641, 647, 653, 661, 673, 677, 691, 701, 709, 733, 739, 743, 773, 787, 797

Offset: 1

Author

N. J. A. Sloane, Dec 25 2017

Keywords

• nonn
• easy

Comments

From Jianing Song, Oct 13 2022: (Start)

Primes p such that kronecker(-163,p) = 1 (or equivalently, kronecker(p,163) = 1).

Primes p such that p^81 == 1 (mod 163). (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

A257362, the sequence of primes that do not remain inert in the field Q(sqrt(-163)), is essentially the same.

Cf. A296915 (rational primes that remain inert in the field Q(sqrt(-163))).

Programs

Maple

Load the Maple program HH given in A296920. Then run HH(-163,200);

PARI

isA296921(p) = isprime(p) && kronecker(p,163) == 1