

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
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OFFSET

1,1


COMMENTS

The "central term" is the term with an index equal to onehalf 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



