A031710 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 32.

257, 1026, 2307, 4100, 6405, 9222, 12551, 16392, 20745, 25610, 30987, 36876, 43277, 50190, 57615, 65552, 74001, 82962, 92435, 102420, 112917, 123926, 135447, 147480, 160025, 173082, 186651, 200732, 215325, 230430, 246047, 262176, 278817, 295970

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

The continued fraction expansion of sqrt((k*m)^2+t*m) for m >= 1 where t divides 2*k has the form [k*m, 2*k/t, 2*k*m, 2*k/t, 2*k*m, ...]. Thus numbers of the form (16*m)^2 + m for m >= 1 are in the sequence. Are there any others? - Chai Wah Wu, Jun 18 2016

The term 297058 is not of the form (16*m)^2 + m. - Chai Wah Wu, Jun 19 2016

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 209 terms from Vincenzo Librandi)

Crossrefs

Cf. A076338.

Programs

Mathematica

Select[Range[10^4], !IntegerQ[Sqrt[#]] && Min[ContinuedFraction[Sqrt[#]][[2]]] == 32 &] (* Vincenzo Librandi, Jun 20 2016 *)

Extensions

Edited by Charles R Greathouse IV, Aug 09 2010

Incorrect formula and comment removed by Vincenzo Librandi, Jan 09 2012

a(34) from Charles R Greathouse IV, Aug 02 2017