login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 5 11:48 EDT 2021. Contains 346467 sequences. (Running on oeis4.)