A288184 Least odd number k such that the continued fraction for sqrt(k) has period n.

5, 3, 41, 7, 13, 19, 73, 31, 113, 43, 61, 103, 193, 179, 109, 133, 157, 139, 337, 151, 181, 253, 853, 271, 457, 211, 949, 487, 821, 379, 601, 463, 613, 331, 1061, 1177, 421, 619, 541, 589, 1117, 571, 1153, 823, 1249, 739, 1069, 631, 1021, 1051, 1201, 751

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Periodic Continued Fraction

Formula

A003285(a(n)) = n, A000035(a(n)) = 1.

Example

a(2) = 3, sqrt(3) = 1 + 1/(1 + 1/(2 + 1/(1 + 1/(2 + 1/...)))), period 2: [1, 2].

Prog

(Python)
from sympy import continued_fraction_periodic
def A288184(n):
    d = 1
    while True:
        s = continued_fraction_periodic(0, 1, d)[-1]
        if isinstance(s, list) and len(s) == n:
            return d
        d += 2 # Chai Wah Wu, Jun 07 2017

Crossrefs

Cf. A000035, A003285, A010337-A010339, A013642-A013644, A013646, A013943, A020347-A020439, A059800, A062769, A097853, A288185.

Sequence in context: A179210 A291843 A187278 * A323779 A343290 A027858

Adjacent sequences: A288181 A288182 A288183 * A288185 A288186 A288187

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 06 2017

Status

approved