A206585 The least number s > 1 having exactly n fives in the periodic part of the continued fraction of sqrt(s).

2, 27, 67, 664, 331, 6487, 1237, 6019, 1999, 6331, 3964, 23983, 4204, 22075, 9739, 64639, 10684, 26419, 17971, 80719, 22969, 140971, 28414, 310759, 34189, 290779, 39181, 228691, 46099, 261691, 56884, 416707, 61429, 136579, 76651, 535375, 75916, 296839, 87151

Offset: 0

Author

T. D. Noe, Mar 19 2012

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A206578 (n ones), A206582 (n twos), A206583 (n threes), A206584 (n fours).

Programs

Mathematica

nn = 50; zeros = nn; t = Table[0, {nn}]; k = 2; While[zeros > 0, If[! IntegerQ[Sqrt[k]], cnt = Count[ContinuedFraction[Sqrt[k]][[2]], 5]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = k; zeros--]]; k++]; Join[{2}, t]

Python

from sympy import continued_fraction_periodic
def A206585(n):
    i = 2
    while True:
        s = continued_fraction_periodic(0,1,i)[-1]
        if isinstance(s, list) and s.count(5) == n:
            return i
        i += 1 # Chai Wah Wu, Jun 10 2017

Extensions

Definition clarified by Chai Wah Wu, Jun 10 2017