A002146 Smallest prime == 7 (mod 8) where Q(sqrt(-p)) has class number 2n+1.

7, 23, 47, 71, 199, 167, 191, 239, 383, 311, 431, 647, 479, 983, 887, 719, 839, 1031, 1487, 1439, 1151, 1847, 1319, 3023, 1511, 1559, 2711, 4463, 2591, 2399, 3863, 2351, 3527, 3719

Offset: 0

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

Comments

Conjecture: a(n) < A002148(n) for all n >= 1. - Jianing Song, Jul 20 2022

References

• D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• David Broadhurst and T. D. Noe, Table of n, a(n) for n = 0..28603
• D. Shanks, Review of R. B. Lakein and S. Kuroda, Tables of class numbers h(-p) for fields Q(sqrt(-p)), p <= 465071, Math. Comp., 24 (1970), 491-492.

Crossrefs

Cf. A002147, A002148, A060651, A002143 (class numbers).

Programs

PARI

a(n) = forprime(p=2, oo, if ((p % 8) == 7, if (qfbclassno(-p) == 2*n+1, return(p)))); \\ Michel Marcus, Jul 20 2022