A102264 Smallest prime for which 2^n exactly divides the class number h(-4p).
5, 17, 41, 257, 521, 4481, 9521, 21929, 72089, 531977, 1256009, 5014169, 20879129, 70993529, 258844361, 866941841, 3771185921, 13949589209, 57388297721
Offset: 1
Links
- H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.
- S. Louboutin, L-functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field, Math. Comp. 59 (1992) 213-230, Table 1.
- A. S. Mosunov and M. J. Jacobson Jr., Unconditional class group tabulation of imaginary quadratic fields to |Δ| < 2^40, Math. Comp. 85 (2016), no. 300, 1983-2009.
Crossrefs
Cf. A006641.
Programs
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Sage
def a(n): for p in Primes(): if QuadraticField(-p).class_number().valuation(2)==n: return p # Robin Visser, May 25 2024
Extensions
a(10)-a(17) from Robin Visser, May 25 2024
a(18)-a(19) from Robin Visser, Dec 28 2024