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

0,1

Links

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

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]

Prog

(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

Crossrefs

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

Sequence in context: A277542 A273844 A294678 * A046735 A038625 A280089

Adjacent sequences: A206582 A206583 A206584 * A206586 A206587 A206588

Keyword

nonn

Author

T. D. Noe, Mar 19 2012

Extensions

Definition clarified by Chai Wah Wu, Jun 10 2017

Status

approved