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%I #27 May 05 2022 11:05:11
%S 0,1,0,0,3,1,0,0,0,4,2,1,0,0,2,0,4,2,2,1,0,0,0,2,0,4,3,2,2,1,0,0,0,0,
%T 0,0,6,6,2,6,2,1,0,0,2,2,2,0,0,4,6,2,2,4,2,1,0,0,4,0,2,2,2,0,4,4,3,6,
%U 2,2,2,1,0,0,0,2,6,0,3,0,0,5,4,6,8,2,2,8,2,1,0,0,6,0,0,4,2,4,4,0,4,4,6,2,7
%N a(n) is the number of 1's in the period of the continued fraction of the square root of the n-th nonsquare integer.
%C For sufficiently large period lengths, the fraction of 1's in the repeating part tends to log(4/3)/log(2) = 0.415... as from the Gauss-Kuzmin distribution, i.e., a(n) tends to 0.415...*A013943(n) for sufficiently large A013943(n). - _A.H.M. Smeets_, Jun 02 2018
%C The "n-th nonsquare integer" in the definition is A005117(n + 1). - _Michael B. Porter_, Jun 06 2018
%H A.H.M. Smeets, <a href="/A099725/b099725.txt">Table of n, a(n) for n = 1..10000</a>
%Y Cf. A005117, A013647, A013943.
%K nonn
%O 1,5
%A _Benoit Cloitre_, Nov 07 2004
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