A002147 -id:A002147 - cp's OEIS frontend

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

N. J. A. Sloane, Mira Bernstein

nonn

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

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).

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.

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

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

A102645 Decimal expansion of (Pi*sqrt(163))^e.

Original entry on oeis.org

2, 2, 8, 0, 6, 9, 9, 9, 2, 3, 8, 5, 5, 6, 1, 3, 9, 2, 7, 1, 7, 0, 3, 8, 9, 8, 9, 3, 4, 4, 3, 3, 1, 1, 1, 5, 1, 1, 7, 5, 8, 8, 1, 6, 6, 2, 5, 0, 8, 3, 3, 0, 3, 9, 9, 3, 7, 4, 4, 7, 4, 0, 3, 5, 4, 9, 0, 6, 9, 5, 6, 0, 6, 3, 3, 0, 7, 3, 3, 9, 1, 2, 6, 7, 5, 7, 3, 1, 7, 2, 7, 4, 4, 7, 2, 9, 8, 4, 0, 6, 8, 8, 8, 8

Offset: 5

Gerald McGarvey, Feb 01 2005

The rounded value of this constant is 22807, a prime of the form p^2 + 6 where p is prime (cf. A079141), a balanced prime of order four (cf. A082079), a smallest prime larger than a square of an n-th prime, a largest prime == 7 mod 8 with class number 2n+1 (cf. A002147) and a prime p such that x^36 = 2 has no solution mod p, but x^12 = 2 has a solution mod p (cf. A059668).

			22806.99923855613927170389893443311151175881662508330399...

Cf. A060295.

RealDigits[(Pi*Sqrt[163])^E, 10, 111][[1]] (* Robert G. Wilson v, Feb 04 2005 *)

cp's OEIS Frontend

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

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