

A083287


Continued fraction expansion of K(3), a constant related to the Josephus problem.


1



1, 1, 1, 1, 1, 1, 5, 10, 19, 1, 4, 4, 4, 3, 10, 1, 42, 2, 23, 33, 1, 4, 7, 1, 12, 1, 1, 2, 9, 2, 11, 3, 4, 1, 1, 3, 2, 4, 25, 3, 1, 16, 5, 10, 1, 1, 1, 3, 1, 1, 1, 3, 2, 2, 1, 1, 1, 2, 3, 2, 1, 3, 4, 3, 1, 1, 117, 2, 1, 12, 4, 1, 4, 3, 3, 15, 1, 5, 16, 7, 2, 7, 21, 1, 3, 1, 2, 2, 2, 1, 1, 1, 1
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OFFSET

1,7


COMMENTS

The constant K(3)=1.62227050288476731595695... is related to the Josephus problem with q=3 and the computation of A054995.


LINKS

Table of n, a(n) for n=1..93.
A. M. Odlyzko and H. S. Wilf, Functional iteration and the Josephus problem, Glasgow Math. J. 33, 235240, 1991.


MATHEMATICA

For[p = 1; nn = 10^4; n = 1, n <= nn, n++, p = Ceiling[3/2*p]]; p/(3/2)^nn // ContinuedFraction[#, 93] & (* JeanFrançois Alcover, Jul 11 2013, after Pari *)


PROG

(PARI) p=1; N=10^4; for(n=1, N, p=ceil(3/2*p)); c=(p/(3/2)^N)+0. \\ This gives K(3) not the sequence!


CROSSREFS

Cf. A054995, A083286.
Sequence in context: A251928 A153370 A119135 * A091922 A030776 A115289
Adjacent sequences: A083284 A083285 A083286 * A083288 A083289 A083290


KEYWORD

nonn,cofr


AUTHOR

Ralf Stephan, Apr 23 2003


STATUS

approved



