A002148 Smallest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1. (Formerly M3164 N1282)

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

0,1

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.

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}]

Crossrefs

Cf. A002143 (class numbers), A002149, A003173, A006203.

Sequence in context: A139874 A155032 A107212 * A290977 A200957 A057175

Adjacent sequences: A002145 A002146 A002147 * A002149 A002150 A002151

Keyword

nonn

Author

N. J. A. Sloane and Mira Bernstein

Extensions

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

Edited by Dean Hickerson, Mar 17 2003

Status

approved