A031742 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 64.

1025, 4098, 9219, 16388, 25605, 36870, 50183, 65544, 82953, 102410, 123915, 147468, 173069, 200718, 230415, 262160, 295953, 331794, 369683, 409620, 451605, 495638, 541719, 589848, 640025, 692250, 746523, 802844, 861213, 921630, 984095, 1048608

Offset

1,1

Comments

The continued fraction expansion of sqrt((j*m)^2+t*m) for m >= 1 where t divides 2*j has the form [j*m, 2*j/t, 2*j*m, 2*j/t, 2*j*m, ...]. Thus numbers of the form (32*m)^2 + m for m >= 1 are in the sequence. Are there any others? - Chai Wah Wu, Jun 18 2016

The term 4464834 is not of the form (32*m)^2 + m. - Chai Wah Wu, Jun 19 2016

Links

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

Mathematica

okQ[n_]:=Module[{sq=Sqrt[n]}, !IntegerQ[sq]&&Min[ContinuedFraction[sq][[2]]]==64]; Select[Range[1100000], okQ] (* Harvey P. Dale, Aug 24 2012 *)

Crossrefs

Sequence in context: A045035 A060948 A171385 * A353943 A351273 A321807

Adjacent sequences: A031739 A031740 A031741 * A031743 A031744 A031745

Keyword

nonn

Author

David W. Wilson

Status

approved