A005474 Class numbers of the real quadratic fields Q(sqrt(A005473(n))).

1, 1, 1, 1, 1, 3, 1, 3, 5, 3, 3, 7, 3, 5, 7, 3, 3, 5, 9, 7, 3, 5, 5, 15, 9, 19, 5, 13, 9, 9, 5, 19, 9, 5, 7, 15, 13, 9, 9, 15, 25, 13, 9, 27, 19, 15, 21, 7, 13, 11, 23, 9, 13, 13, 11, 33, 15, 25, 23, 15, 13, 29, 21, 17, 43, 35, 27, 33, 17, 17, 27, 45, 11, 63, 15, 31, 17, 15, 33, 15, 31, 31

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• Robin Visser, Table of n, a(n) for n = 1..10000
• D. Shanks, The simplest cubic fields, Math. Comp., 28 (1974), 1137-1152 (see Table 2 page 1143).
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A005472, A005473.

Programs

Sage

def a(n):
    m, k = 1, 1
    while (m < n): k += 1; m += (k^2+4).is_prime()
    return QuadraticField(k^2+4).class_number()  # Robin Visser, Dec 07 2024

Extensions

More terms and name edited by Robin Visser, Dec 07 2024