A031414 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 1.

13, 29, 53, 58, 74, 85, 97, 106, 125, 137, 157, 173, 185, 229, 233, 241, 293, 298, 314, 338, 346, 353, 365, 389, 397, 425, 433, 445, 457, 461, 533, 538, 541, 554, 557, 593, 629, 634, 641, 661, 673, 698, 733, 746, 754, 769, 794, 818, 821, 829, 845, 857, 877

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Examples

			The continued fraction of sqrt[29] is {5; 2, 1, 1, 2, 10}. The center number in the periodic part is 1.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A031404-A031423.

Subsequence of A003814.

Programs

Mathematica

n = 1; t = {}; While[Length[t] < 60, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 1, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 03 2014 *)

Extensions

Initial 2 removed by T. D. Noe, Apr 03 2014

Definitions of A031414-A031423 clarified by N. J. A. Sloane, Aug 18 2021