%I #21 Aug 07 2024 10:12:41

%S 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,

%T 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,

%U 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

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

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

%H A. M. Odlyzko and H. S. Wilf, <a href="https://doi.org/10.1017/S0017089500008272">Functional iteration and the Josephus problem</a>, Glasgow Math. J. 33, 235-240, 1991.

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%t 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 *)

%o (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!

%Y Cf. A054995, A083286 (decimal expansion).

%K nonn,cofr

%O 0,7

%A _Ralf Stephan_, Apr 23 2003

%E Offset changed by _Andrew Howroyd_, Aug 07 2024