A031421 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 8.

509, 1450, 2237, 2425, 3946, 4778, 5189, 5473, 5618, 5914, 6445, 6761, 7417, 8185, 9178, 9938, 10133, 10426, 10529, 10826, 10933, 11441, 11861, 12074, 12289, 12506, 12829, 13273, 14653, 14765, 15241, 16217, 16586, 16837, 17090, 17989, 18385, 18650, 18778

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000 [shifted by Georg Fischer, Jun 23 2019]

Mathematica

n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 8 && c[[2, (len + 1)/2 - 1]] == 8, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014; adapted by Georg Fischer, Jun 23 2019 *)

Crossrefs

Cf. A031404-A031423.

Subsequence of A003814.

Sequence in context: A256709 A110025 A059763 * A255183 A126438 A126582

Adjacent sequences: A031418 A031419 A031420 * A031422 A031423 A031424

Keyword

nonn

Author

David W. Wilson

Extensions

a(1) corrected by T. D. Noe, Apr 04 2014

Data adapted to new definition by Georg Fischer, Jun 23 2019

Status

approved