

A031710


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


1



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
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OFFSET

1,1


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)


MATHEMATICA

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


CROSSREFS

Cf. A076338.
Sequence in context: A105131 A202372 A036549 * A253419 A070184 A054801
Adjacent sequences: A031707 A031708 A031709 * A031711 A031712 A031713


KEYWORD

nonn


AUTHOR

David W. Wilson


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


STATUS

approved



