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

Author

Ralf Stephan, Apr 23 2003

Keywords

• nonn
• cofr

Comments

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

Links

• 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

Crossrefs

Cf. A054995, A083286 (decimal expansion).

Programs

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 *)

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!

Extensions

Offset changed by Andrew Howroyd, Aug 07 2024