A031766 - OEIS

%I #19 Jul 16 2021 02:37:54

%S 1937,7746,17427,30980,48405,69702,94871,123912,156825,193610,234267,

%T 278796,327197,379470,435615,495632,559521,627282,698915,774420,

%U 853797,937046,1024167,1115160,1210025,1308762,1411371,1517852,1628205,1742430

%N Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 88.

%C From _Chai Wah Wu_, Nov 07 2016: (Start)

%C If r is even, then the least term of the continued fraction of (r*m/2)^2+m is r for all m >= 1. On the other hand, the least term of the continued fraction of r^4/4 + r^3 + 2r^2 + 3r+2 is also r but it is not of the form (r*m/2)^2+m.

%C If r is odd, then the least term of the continued fraction of (r*m)^2+2m is r for all m >= 1 and the least term of the continued fraction of r^4 + r^3 + 5*(r+1)^2/4 is also r but it is not of the form (r*m)^2+2m.

%C This means that 1936*m^2 + m are terms of the sequence for all m >= 1 and 15689610 is also a term but not of the form 1936*m^2 + m.

%C (End)

%H Charles R Greathouse IV, <a href="/A031766/b031766.txt">Table of n, a(n) for n = 1..10000</a>

%K nonn

%O 1,1

%A _David W. Wilson_