A369863 Inert rational primes in the field Q(sqrt(-21)).

13, 29, 43, 47, 53, 59, 61, 67, 73, 79, 83, 97, 113, 127, 131, 137, 149, 151, 157, 163, 167, 181, 197, 211, 227, 229, 233, 241, 251, 281, 311, 313, 317, 331, 349, 379, 383, 389, 397, 401, 409, 419, 433, 449, 463, 467, 479, 487, 499, 503, 547, 557, 563, 569, 571, 577, 587

Offset

1,1

Comments

Primes p such that Legendre(-21,p) = -1.

Links

Table of n, a(n) for n=1..57.

Mathematica

Select[Range[3, 600], PrimeQ[#] && JacobiSymbol[-21, #]==-1 &] (* Stefano Spezia, Feb 04 2024 *)

Prog

(SageMath) [p for p in prime_range(3, 600) if legendre_symbol(-21, p) == -1]

Crossrefs

Cf. inert rational primes in the imaginary quadratic field Q(sqrt(-d)) for the first squarefree positive integers d: A002145 (1), A003628 (2), A003627 (3), A003626 (5), A191059 (6), A003625 (7), A296925 (10), A191060 (11), A105885 (13), A191061 (14), A191062 (15), A296930 (17), A191063 (19), this sequence (21), A191064 (22), A191065 (23).

Sequence in context: A352926 A339989 A120827 * A320631 A339113 A309356

Adjacent sequences: A369860 A369861 A369862 * A369864 A369865 A369866

Keyword

nonn

Author

Dimitris Cardaris, Feb 03 2024

Status

approved