A102269 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = +1.

43, 67, 79, 127, 151, 163, 211, 331, 379, 463, 487, 499, 547, 571, 631, 739, 751, 823, 883, 907, 919, 967, 991, 1051, 1087, 1171, 1303, 1327, 1423, 1471, 1579, 1663, 1723, 1747, 1759, 1831, 1999, 2011, 2083, 2143, 2179, 2251, 2311, 2347, 2503, 2647, 2671, 2683, 2731, 2767, 2851, 3019

Offset

1,1

Comments

Primes p such that p is 3 (mod 4) and (-3/p) = (-7/p) = 1, where (k/n) is the Kronecker symbol. - Robin Visser, Mar 13 2024

Links

Table of n, a(n) for n=1..52.

H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.

Formula

The primes are congruent to {43, 67, 79} (mod 84). - Robin Visser, Mar 13 2024

Prog

(Magma) [p : p in PrimesUpTo(3000) | p mod 84 in [43, 67, 79]];  // Robin Visser, Mar 13 2024

Crossrefs

Cf. A102270, A102271, A102272, A102273, A102274, A102275.

Sequence in context: A253848 A245742 A295702 * A020349 A050959 A273773

Adjacent sequences: A102266 A102267 A102268 * A102270 A102271 A102272

Keyword

nonn

Author

N. J. A. Sloane, Feb 19 2005

Extensions

More terms from Robin Visser, Mar 13 2024

Status

approved