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 A031557 that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 59. 1
 3483, 3491, 3499, 3511, 3527, 3539, 3547, 3559, 3571, 3579, 3583, 3587, 3607, 3623, 3631, 3643, 3647, 3651, 3659, 3667, 3671, 3691, 3699, 3707, 3719, 13928, 13952, 13960, 13984, 14016, 14080, 14120, 14152, 14176, 14208, 14216, 14240, 14248, 14304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 MATHEMATICA cfep59Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 59]; Select[Range[15000], cfep59Q] (* Harvey P. Dale, Feb 18 2016 *) PROG (Python) from __future__ import division from sympy import continued_fraction_periodic A031557_list = [n for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in range(1, 10**5)) if isinstance(s, list) and len(s) % 2 == 0 and s[len(s)//2-1] == 59] # Chai Wah Wu, Jun 08 2017 CROSSREFS Sequence in context: A176380 A156773 A174753 * A031737 A268156 A180994 Adjacent sequences: A031554 A031555 A031556 * A031558 A031559 A031560 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 26 06:47 EDT 2023. Contains 361529 sequences. (Running on oeis4.)