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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Cf. A139492, A141159.

Sequence in context: A016041 A140797 A245730 * A191064 A075227 A350880

Adjacent sequences: A038890 A038891 A038892 * A038894 A038895 A038896

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Name clarified by Michel Marcus, Jun 22 2019

Status

approved