A031740 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 62.

962, 3846, 8652, 15380, 24030, 34602, 47096, 61512, 77850, 96110, 116292, 138396, 162422, 188370, 216240, 246032, 277746, 311382, 346940, 384420, 423822, 465146, 508392, 553560, 600650, 649662, 700596, 753452, 808230, 864930, 923552, 984096

Offset

1,1

Comments

a(n) = 961n^2 + n for n < 65, but a(65) = 3940288. - Charles R Greathouse IV, Aug 04 2017

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

Conjecture: a(n) = n*(961*n+1). a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: 2*x*(481+480*x)/(1-x)^3. - Colin Barker, Sep 30 2012

Conjecture is false. m*(961*m+1) for m >= 1 is a subsequence (see comment in A031712) and 3940288 is a term not of the form m*(961*m+1). - Chai Wah Wu, Jun 19 2016

Mathematica

Select[Range[10^6], !IntegerQ[Sqrt[#]]&&Min[ContinuedFraction[Sqrt[#]][[2]]] == 62 &] (* Vincenzo Librandi, Jun 20 2016 *)

Crossrefs

Sequence in context: A304315 A393861 A158414 * A031529 A347884 A031709

Adjacent sequences: A031737 A031738 A031739 * A031741 A031742 A031743

Keyword

nonn

Author

David W. Wilson

Status

approved