A102264 - OEIS

%I #12 May 25 2024 21:05:46

%S 5,17,41,257,521,4481,9521,21929,72089,531977,1256009,5014169,

%T 20879129,70993529,258844361,866941841,3771185921

%N Smallest prime for which 2^n exactly divides the class number h(-4p).

%H H. Cohn and J. C. Lagarias, <a href="http://dx.doi.org/10.1090/S0025-5718-1983-0717716-8">On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies</a>, Math. Comp. 41 (1983), 711-730.

%H S. Louboutin, <a href="http://dx.doi.org/10.1090/S0025-5718-1992-1134735-6">L-functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field</a>, Math. Comp. 59 (1992) 213-230, Table 1

%o (Sage)

%o def a(n):

%o     for p in Primes():

%o         if QuadraticField(-p).class_number().valuation(2)==n:

%o             return p  # _Robin Visser_, May 25 2024

%Y Cf. A006641.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Feb 19 2005

%E a(10)-a(17) from _Robin Visser_, May 25 2024