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 A031597 Numbers k such 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 99. 1
 9803, 9811, 9839, 9843, 9851, 9859, 9871, 9883, 9887, 9899, 9907, 9923, 9931, 9959, 9963, 9967, 9987, 9991, 10007, 10019, 10031, 10039, 10067, 10079, 10083, 10091, 10099, 10103, 10107, 10111, 10131, 10139, 10147, 10151, 10159, 10163, 10199, 39208 (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 ep99Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[s][[2]]]; len= Length[ cf]; EvenQ[len]&&cf[[len/2]]==99]; Select[Range[40000], ep99Q] (* Harvey P. Dale, May 07 2023 *) PROG (Python) from __future__ import division from sympy import continued_fraction_periodic A031597_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] == 99] # Chai Wah Wu, Jun 10 2017 CROSSREFS Sequence in context: A113937 A036353 A174769 * A031777 A237064 A251977 Adjacent sequences: A031594 A031595 A031596 * A031598 A031599 A031600 KEYWORD nonn AUTHOR David W. Wilson EXTENSIONS Definition corrected by Harvey P. Dale, May 07 2023 STATUS approved

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Last modified August 11 14:00 EDT 2024. Contains 375069 sequences. (Running on oeis4.)