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A206585
The least number s > 1 having exactly n fives in the periodic part of the continued fraction of sqrt(s).
5
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
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Mar 19 2012
EXTENSIONS
Definition clarified by Chai Wah Wu, Jun 10 2017
STATUS
approved