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A031712 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 34. 3

%I

%S 290,1158,2604,4628,7230,10410,14168,18504,23418,28910,34980,41628,

%T 48854,56658,65040,74000,83538,93654,104348,115620,127470,139898,

%U 152904,166488,180650,195390,210708,226604,243078,260130,277760,295968,314754,334118,354060,374580,375804

%N Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 34.

%C 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 (17*m)^2 + m for m >= 1 are in the sequence. Are there any others? - _Chai Wah Wu_, Jun 18 2016

%C The term 375804 is not of the form (17*m)^2 + m. - _Chai Wah Wu_, Jun 19 2016

%H Charles R Greathouse IV, <a href="/A031712/b031712.txt">Table of n, a(n) for n = 1..10000</a>

%K nonn

%O 1,1

%A _David W. Wilson_

%E a(35)-a(37) from _Charles R Greathouse IV_, Aug 03 2017

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Last modified October 19 09:36 EDT 2021. Contains 348074 sequences. (Running on oeis4.)