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 A031598 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 100. 2
 10002, 10006, 10018, 10022, 10046, 10054, 10078, 10082, 10086, 10102, 10118, 10134, 10146, 10162, 10174, 10178, 10182, 10194, 10198, 10214, 10226, 10238, 10274, 10278, 10294, 10306, 10326, 10334, 10338, 10342, 10358, 10402, 22503, 22521, 22548, 22557 (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 cf100Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[s][[2]]]; len= Length[ cf]; EvenQ[len]&&cf[[(len)/2]]==100]; Select[Range[23000], cf100Q] PROG (Python) from __future__ import division from sympy import continued_fraction_periodic A031598_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] == 100] # Chai Wah Wu, Jun 10 2017 CROSSREFS Sequence in context: A364050 A360574 A330135 * A210760 A164968 A165296 Adjacent sequences: A031595 A031596 A031597 * A031599 A031600 A031601 KEYWORD nonn AUTHOR David W. Wilson EXTENSIONS Definition corrected by Harvey P. Dale, Jul 13 2023 STATUS approved

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Last modified August 15 04:20 EDT 2024. Contains 375172 sequences. (Running on oeis4.)