A083287 Continued fraction expansion of K(3), a constant related to the Josephus problem.

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

Offset

0,7

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=0..92.

A. M. Odlyzko and H. S. Wilf, Functional iteration and the Josephus problem, Glasgow Math. J. 33, 235-240, 1991.

Index entries for sequences related to the Josephus Problem

Mathematica

For[p = 1; nn = 10^4; n = 1, n <= nn, n++, p = Ceiling[3/2*p]]; p/(3/2)^nn // ContinuedFraction[#, 93] & (* Jean-François 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 (decimal expansion).

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

Extensions

Offset changed by Andrew Howroyd, Aug 07 2024

Status

approved