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A031539 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 41. 0
1683, 1687, 1691, 1699, 1707, 1723, 1747, 1759, 1779, 1783, 1787, 1799, 1811, 1819, 1823, 1831, 1843, 1847, 6728, 6752, 6784, 6824, 6848, 6856, 6880, 6912, 6920, 6944, 6976, 7008, 7016, 7040, 7072, 7104, 7168, 7240, 7264, 7328, 7360, 7392, 15135, 15195 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The "central term" is the term with an index equal to one-half of the length of the continued fraction's period. For example, the "central term" of (1,2,3,4) is 2. - Harvey P. Dale, Nov 10 2017

LINKS

Table of n, a(n) for n=1..42.

MATHEMATICA

ct41Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1, 1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 41]; Select[Range[16000], ct41Q] (* Harvey P. Dale, Nov 10 2017 *)

CROSSREFS

Sequence in context: A204568 A035766 A107562 * A205739 A031719 A206671

Adjacent sequences:  A031536 A031537 A031538 * A031540 A031541 A031542

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 18 13:34 EDT 2021. Contains 348067 sequences. (Running on oeis4.)