This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A031710 #49 Jul 15 2021 01:50:06 %S A031710 257,1026,2307,4100,6405,9222,12551,16392,20745,25610,30987,36876, %T A031710 43277,50190,57615,65552,74001,82962,92435,102420,112917,123926, %U A031710 135447,147480,160025,173082,186651,200732,215325,230430,246047,262176,278817,295970 %N A031710 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 32. %C A031710 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 %C A031710 The term 297058 is not of the form (16*m)^2 + m. - _Chai Wah Wu_, Jun 19 2016 %H A031710 Charles R Greathouse IV, <a href="/A031710/b031710.txt">Table of n, a(n) for n = 1..10000</a> (first 209 terms from Vincenzo Librandi) %t A031710 Select[Range[10^4], !IntegerQ[Sqrt[#]] && Min[ContinuedFraction[Sqrt[#]][[2]]] == 32 &] (* _Vincenzo Librandi_, Jun 20 2016 *) %Y A031710 Cf. A076338. %K A031710 nonn %O A031710 1,1 %A A031710 _David W. Wilson_ %E A031710 Edited by _Charles R Greathouse IV_, Aug 09 2010 %E A031710 Incorrect formula and comment removed by _Vincenzo Librandi_, Jan 09 2012 %E A031710 a(34) from _Charles R Greathouse IV_, Aug 02 2017