A031539 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 41.

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

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