A031414 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A031404-A031423.

Subsequence of A003814.

Sequence in context: A153422 A166034 A370238 * A270361 A010337 A244637

Adjacent sequences: A031411 A031412 A031413 * A031415 A031416 A031417

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

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

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

STATUS

approved