A002149 Largest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1. (Formerly M5407 N2350)

163, 907, 2683, 5923, 10627, 15667, 20563, 34483, 37123, 38707, 61483, 90787, 93307, 103387, 166147, 133387, 222643, 210907, 158923, 253507, 296587

Offset

0,1

Comments

Most of these values are only conjectured to be correct.

Apr 15 2008: David Broadhurst says: I computed class numbers for prime discriminants with |D| < 10^9, but stopped when the first case with |D| > 5*10^8 was observed. That factor of 2 seems to me to be a reasonable margin of error, when you look at the pattern of what is included.

Arno, Robinson, & Wheeler prove a(0)-a(11). - Charles R Greathouse IV, Apr 25 2013

References

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, Table of n, a(n) for n = 0..739 (conjectural; see comment)

Steven Arno, M. L. Robinson, and Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998), pp. 295-330.

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. A002148, A003173, A006203.

Sequence in context: A127883 A054466 A221903 * A167627 A109343 A217644

Adjacent sequences: A002146 A002147 A002148 * A002150 A002151 A002152

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by Dean Hickerson, Mar 17 2003

Status

approved