A031676 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 88.

96149, 160081, 238265, 334253, 438469, 441121, 445114, 562789, 565793, 705961, 709325, 712697, 1036853, 1040929, 1045013, 1212826, 1215029, 1219441, 1223861, 1230506, 1237169, 1416829, 1639241, 1644365, 1659785, 1664941, 1875122

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Example

The c.f. expansion of sqrt(96149) is 310, [12, 1, 1, 1, 8, 1, 1, 2, 21, 1, 3, 21, 1, 8, 1, 1, 2, 2, 2, 2, 1, 3, 154, 1, 3, 2, 1, 10, 1, 1, 2, 1, 1, 88, 88, 1, 1, 2, 1, 1, 10, 1, 2, 3, 1, 154, 3, 1, 2, 2, 2, 2, 1, 1, 8, 1, 21, 3, 1, 21, 2, 1, 1, 8, 1, 1, 1, 12, 620], [12, 1, 1, 1, 8, 1, 1, 2, 21, 1, 3, 21, 1, 8, 1, 1, 2, 2, 2, 2, 1, 3, 154, 1, 3, 2, 1, 10, 1, 1, 2, 1, 1, 88, 88, 1, 1, 2, 1, 1, 10, 1, 2, 3, 1, 154, 3, 1, 2, 2, 2, 2, 1, 1, 8, 1, 21, 3, 1, 21, 2, 1, 1, 8, 1, 1, 1, 12, 620], ..., where two copies of the period are shown. If the term 620 is deleted, the two central terms of the period are 88. So 96149 is a term. - N. J. A. Sloane, Aug 18 2021

Mathematica

cf88Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[s][[2]]]; len=Length[cf]; OddQ[len] && cf[[(len+1)/2]] == 88]; Select[Range[1875200], cf88Q] (* Harvey P. Dale, Aug 17 2021 *)

Crossrefs

Sequence in context: A116265 A270149 A270116 * A205613 A205351 A343282

Adjacent sequences: A031673 A031674 A031675 * A031677 A031678 A031679

Keyword

nonn

Author

David W. Wilson

Extensions

First term 7745 removed by Georg Fischer, Jun 16 2019

Name clarified by N. J. A. Sloane, Aug 18 2021

Status

approved