%I A013645
%S A013645 1,2,3,7,13,19,31,43,46,94,139,151,166,211,331,421,526,571,604,631,751,
               886,
%T A013645 919,1291,1324,1366,1516,1621,1726,2011,2311,2566,2671,3004,3019,3334,
%U A013645 3691,3931,4174,4846,5119,6211,6451,6679,6694,7606,8254,8779,8941,9739
%N A013645 Values of n at which period of continued fraction for sqrt(n) increases.
%D A013645 Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 
               1984, page 426 (but beware of errors!).
%H A013645 T. D. Noe, <a href="b013645.txt">Table of n, a(n) for n=1..200</a>
%e A013645 The continued fraction for Sqrt(31) is 5, {1, 1, 3, 5, 3, 1, 1, 10} and 
               the continued fraction for Sqrt(43) is 6, {1, 1, 3, 1, 5, 1, 3, 1, 
               1, 12}; and there is no number between 31 and 43 whose square root 
               produces a continued fraction the period of which exceeds the one 
               for 31.
%t A013645 a = -1; Do[l = Length[ Last[ ContinuedFraction[ Sqrt[ n]]]]; If[ l > 
               a, a = l; Print[n]], {n, 1, 10^4} ]
%Y A013645 Cf. A003285.
%Y A013645 Sequence in context: A101415 A045331 A053613 this_sequence A130272 A038940 
               A019383
%Y A013645 Adjacent sequences: A013642 A013643 A013644 this_sequence A013646 A013647 
               A013648
%K A013645 nonn,nice
%O A013645 1,2
%A A013645 Clark Kimberling (ck6(AT)evansville.edu)
%E A013645 More terms from David W. Wilson (davidwwilson(AT)comcast.net)