login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038893 Odd primes p such that 21 is a square mod p. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A016041 A140797 A245730 * A191064 A075227 A350880
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name clarified by Michel Marcus, Jun 22 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)