A038893 Odd primes p such that 21 is a square mod p.

3, 5, 7, 17, 37, 41, 43, 47, 59, 67, 79, 83, 89, 101, 109, 127, 131, 151, 163, 167, 173, 193, 211, 227, 251, 257, 269, 277, 293, 311, 331, 337, 353, 373, 379, 383, 419, 421, 457, 461, 463, 467, 479, 487, 499, 503

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These primes correspond to the representation of the two classes of discriminant 21 of binary quadratic forms with principal reduced forms [1, 3, -3] and [3, 3, -1]. The first class represents the primes given in A141159 (or A139492). The second class gives the prime 3 (which divides 21), and primes congruent to 2 (mod 3) and also to 3, 5, 6 (mod 7). The solution of x^2 - 21 == 0 (mod p) leads to the representative primitive parallel forms for discriminant 21 and representation of primes p. - Wolfdieter Lang, Jun 19 2019

Prime factors of A082111 and excluding the 3, prime factors of A004538. - Klaus Purath, Jan 04 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A139492, A141159.

Programs

Mathematica

Select[Prime[Range[100]], JacobiSymbol[21, #] != -1 &] (* Vincenzo Librandi, Sep 07 2012 *)

PARI

isok(p) = (p>2) && isprime(p) && issquare(Mod(21, p)); \\ Michel Marcus, Jun 19 2019

Extensions

Name clarified by Michel Marcus, Jun 22 2019