A288185 Least even number k such that the continued fraction for sqrt(k) has period n.

2, 6, 130, 14, 74, 22, 58, 44, 106, 86, 298, 46, 746, 134, 1066, 94, 1018, 424, 922, 268, 394, 166, 586, 382, 1306, 214, 1354, 334, 1642, 436, 2122, 508, 1114, 454, 4138, 478, 3194, 1108, 4874, 526, 3418, 724, 2458, 604, 9914, 694, 4618, 844, 2746, 1318

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)) = 0.

Example

a(2) = 6, sqrt(6) = 2 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/...)))), period 2: [2, 4].

Prog

(Python)
from sympy import continued_fraction_periodic
def A288185(n):
    d = 2
    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 08 2017

Crossrefs

Cf. A000035, A003285, A010337-A010339, A013642-A013644, A013646, A013943, A020347-A020439, A097853, A240072, A288184.

Sequence in context: A060001 A181316 A101753 * A359961 A274695 A392768

Adjacent sequences: A288182 A288183 A288184 * A288186 A288187 A288188

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 06 2017

Status

approved