%I #37 Jul 11 2021 14:32:26
%S 3,8,15,24,35,48,63,80,99,120,143,168,175,176,195,208,224,255,288,323,
%T 360,399,440,483,528,551,575,624,675,728,783,799,840,899,960,1023,
%U 1035,1088,1155,1224,1247,1295,1368,1403,1443,1520,1599,1680,1763,1848,1872
%N Numbers k such that the periodic part of the continued fraction for sqrt(k) contains a single 1.
%C All the terms of A005563 are here, as well as some additional terms (with even period > 2 and the digit 1 in central position) (e.g., sqrt(175) = [13,'4, 2, 1, 2, 4, 26']).
%D Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).
%H T. D. Noe, <a href="/A013648/b013648.txt">Table of n, a(n) for n = 1..1000</a>
%H R. Macmillan, <a href="http://www.jstor.org/stable/3621471">Continued fractions</a>, Math. Gaz. 84, 2000. See p. 34.
%t Select[ Range@ 1900, !IntegerQ[ Sqrt@ #] && Count[ ContinuedFraction[ Sqrt@ #][[2]], 1] == 1 &] (* _Robert G. Wilson v_, Jul 03 2011 *)
%Y Union of A005563 and A102538.
%Y Cf. A040001, A040005, A040011, A040019, A040029, A062196.
%K nonn
%O 1,1
%A _Clark Kimberling_
%E Additional comments from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 30 2001
%E Incorrect formulas and programs removed by _R. J. Mathar_, Jan 06 2011