A002148 Smallest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1.

3, 59, 131, 251, 419, 659, 1019, 971, 1091, 2099, 1931, 1811, 3851, 3299, 2939, 3251, 4091, 4259, 8147, 5099, 9467, 6299, 6971, 8291, 8819, 14771, 22619, 9539, 13331, 18443, 11171, 16979, 12011, 13859, 16931, 17939, 28211, 19211, 24251, 20411

Offset: 0

Author

N. J. A. Sloane and Mira Bernstein

Keywords

• nonn

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..10399
• 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. A002143 (class numbers), A002149, A003173, A006203.

Programs

Mathematica

a=Table[0, {101}]; Do[If[PrimeQ[m], c=NumberFieldClassNumber[Sqrt[-m]]; If[c<102 && a[[c]]==0, a[[c]]=m]], {m, 3, 30000, 8}]; Table[a[[n]], {n, 1, 101, 2}]

Extensions

More terms from Robert G. Wilson v, Apr 17 2001

Edited by Dean Hickerson, Mar 17 2003