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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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,...].

LINKS

Table of n, a(n) for n=1..104.

CROSSREFS

Cf. A084576-A084579, A084581-A084587.

Sequence in context: A030305 A228350 A220482 * A263633 A171850 A087782

Adjacent sequences:  A084577 A084578 A084579 * A084581 A084582 A084583

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 31 2003

STATUS

approved

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Last modified May 26 22:57 EDT 2019. Contains 323597 sequences. (Running on oeis4.)