%I #15 Jun 23 2020 17:34:55

%S 1,1,1,3,2,6,5,1,3,10,7,9,1,2,6,5,17,18,11,13,15,10,2,1,11,10,7,9,17,

%T 30,31,31,19,22,22,27,26,23,18,1,1,1,6,19,17,18,17,13,15,14,30,29,53,

%U 50,55,55,50,33,34,38,38,39,49,47,46,46,41,29,31,1,2,6,1,1,3,10,34,34,34,30

%N The survivor w(n,4) in a modified Josephus problem, with a step of 4.

%H Chris Groër, <a href="http://www.jstor.org/stable/3647800">The Mathematics of Survival: From Antiquity to the Playground</a>, Amer. Math. Monthly, 110(9) (2003), 812-825.

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

%t w4[1] = v4[1] = u4[1] = 1; w4[n_] := w4[n] = Switch[ Mod[n, 4], 0, n + 1 - Ceiling[4w4[ Ceiling[3n/4]]/3], 1, n + 1 - Floor[(4w4[ Ceiling[3n/4]] + 1)/3], 2, n + 1 - Floor[4v4[ Ceiling[3n/4]]/3], 3, n + 1 - Floor[(4u4[ Ceiling[3n/4]] - 1)/3]]; v4[n_] := v4[n] = Switch[ Mod[n, 4], 0, n + 1 - Floor[(4w4[ Ceiling[3n/4]] + 1)/3], 1, n + 1 - Floor[(4v4[ Ceiling[3n/4]])/3], 2, n + 1 - Floor[(4u4[ Ceiling[3n/4]] - 1)/3], 3, n + 1 - Ceiling[ 4w4[ Floor[3n/4]]/3]]; u4[n_] := u4[n] = Switch[ Mod[n, 4], 0, n + 1 - Floor[ 4v4[ Ceiling[3n/4]]/3], 1, n + 1 - Floor[ (4u4[ Ceiling[3n/4]] - 1)/3], 2, n + 1 - Ceiling[ 4w4[ Floor[3n/4]]/3], 3, n + 1 - Floor[(4w4[ Floor[3n/4]] + 1)/3]]; Table[ w4[n], {n, 81}] (* from Chris Groer modified by _Robert G. Wilson v_ Nov 15 2003 *)

%Y Cf. A006257, A088442, A088443, A090569.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Nov 09 2003

%E Terms computed by Chris Groer (cgroer(AT)math.uga.edu)