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A206585
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The least number s > 1 having exactly n fives in the periodic part of the continued fraction of sqrt(s).
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5
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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
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OFFSET
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0,1
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LINKS
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MATHEMATICA
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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]
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PROG
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(Python)
from sympy import continued_fraction_periodic
i = 2
while True:
s = continued_fraction_periodic(0, 1, i)[-1]
if isinstance(s, list) and s.count(5) == n:
return i
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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