login
Smallest prime == 7 (mod 8) where Q(sqrt(-p)) has class number 2n+1.
(Formerly M4377 N1841)
7

%I M4377 N1841 #32 Aug 06 2022 07:17:22

%S 7,23,47,71,199,167,191,239,383,311,431,647,479,983,887,719,839,1031,

%T 1487,1439,1151,1847,1319,3023,1511,1559,2711,4463,2591,2399,3863,

%U 2351,3527,3719

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

%C Conjecture: a(n) < A002148(n) for all n >= 1. - _Jianing Song_, Jul 20 2022

%D D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David Broadhurst and T. D. Noe, <a href="/A002146/b002146.txt">Table of n, a(n) for n = 0..28603</a>

%H D. Shanks, <a href="https://doi.org/10.1090/S0025-5718-70-99853-4">Review of R. B. Lakein and S. Kuroda, Tables of class numbers h(-p) for fields Q(sqrt(-p)), p <= 465071</a>, Math. Comp., 24 (1970), 491-492.

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

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

%K nonn

%O 0,1

%A _N. J. A. Sloane_, _Mira Bernstein_