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

Author

N. J. A. Sloane, Feb 19 2005

Keywords

• nonn
• more

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

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