

A031742


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


4



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



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 * A321807 A017683 A013958
Adjacent sequences: A031739 A031740 A031741 * A031743 A031744 A031745


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



