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Smallest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1.
(Formerly M3164 N1282)
14

%I M3164 N1282 #29 Aug 06 2022 07:17:33

%S 3,59,131,251,419,659,1019,971,1091,2099,1931,1811,3851,3299,2939,

%T 3251,4091,4259,8147,5099,9467,6299,6971,8291,8819,14771,22619,9539,

%U 13331,18443,11171,16979,12011,13859,16931,17939,28211,19211,24251,20411

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

%D D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David Broadhurst and T. D. Noe, <a href="/A002148/b002148.txt">Table of n, a(n) for n = 0..10399</a>

%H D. Shanks, <a href="https://doi.org/10.1090/S0025-5718-70-99853-4">Review of R. B. Lakein and S. Kuroda, Tables of class numbers h(-p) for fields Q(sqrt(-p)), p <= 465071</a>, Math. Comp., 24 (1970), 491-492.

%t 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}]

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

%K nonn

%O 0,1

%A _N. J. A. Sloane_ and _Mira Bernstein_

%E More terms from _Robert G. Wilson v_, Apr 17 2001

%E Edited by _Dean Hickerson_, Mar 17 2003