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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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.

Extensions

Edited by Dean Hickerson, Mar 17 2003