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

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

Cf. A031404-A031423.

Subsequence of A003814.

Programs

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 *)

Extensions

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

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