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 A084580 Let y = m/GK(k), where m and k vary over the positive integers and GK(k)=log(1+1/(k*(k+2))/log(2) is the Gauss-Kuzmin distribution of k. Sort the y values by size and number them consecutively by n. This sequence gives the values of k in order by n. 2

%I

%S 1,1,2,1,1,3,2,1,1,1,4,2,1,3,1,2,1,5,1,1,2,1,3,6,1,4,2,1,1,1,2,3,1,7,

%T 1,2,1,5,1,4,2,1,3,1,8,1,2,1,1,3,2,1,6,1,4,9,1,2,1,5,1,3,2,1,1,1,2,10,

%U 1,4,3,1,7,2,1,1,1,2,1,3,5,1,11,2,6,1,4,1,2,1,3,1,1,8,2,1,1,12,2,1,3,4,1,1

%N Let y = m/GK(k), where m and k vary over the positive integers and GK(k)=log(1+1/(k*(k+2))/log(2) is the Gauss-Kuzmin distribution of k. Sort the y values by size and number them consecutively by n. This sequence gives the values of k in order by n.

%C The geometric mean of the sequence equals Khintchine's constant K=2.685452001 since the frequency of the integers agrees with the Gauss-Kuzmin distribution. When considered as a continued fraction, the resulting constant is 0.5815803358828329856145... = [0;1,1,2,1,1,3,2,1,1,1,4,2,1,...].

%Y Cf. A084576-A084579, A084581-A084587.

%K nonn

%O 1,3

%A _Paul D. Hanna_, May 31 2003

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Last modified January 18 14:40 EST 2022. Contains 350455 sequences. (Running on oeis4.)