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A084580
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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.
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3
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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, 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, 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
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OFFSET
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1,3
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COMMENTS
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The geometric mean of the sequence equals Khintchine's constant K=2.685452001 = A002210 since the frequency of the integers agrees with the Gauss-Kuzmin distribution. When considered as a continued fraction, the resulting constant is 0.5815803358828329856145... = A372869 = [0;1,1,2,1,1,3,2,1,1,1,4,2,1,...].
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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