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A181281 A version of Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,...,n in a circle, increasing clockwise. Starting with i=1, delete the integer 4 places clockwise from i. Repeat, counting 4 places from the next undeleted integer, until only one integer remains. 5

%I

%S 1,2,1,2,2,1,6,3,8,3,8,1,6,11,1,6,11,16,2,7,12,17,22,3,8,13,18,23,28,

%T 3,8,13,18,23,28,33,1,6,11,16,21,26,31,36,41,46,4,9,14,19,24,29,34,39,

%U 44,49,54,1,6,11,16,21,26,31,36,41,46,51,56,61,66,71,3,8,13,18,23,28,33,38

%N A version of Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,...,n in a circle, increasing clockwise. Starting with i=1, delete the integer 4 places clockwise from i. Repeat, counting 4 places from the next undeleted integer, until only one integer remains.

%D Paul Weisenhorn, Josephus und seine Folgen, MNU Journal (Der mathematische und naturwissenschaftliche Unterricht), 59 (2006), 18-19.

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

%F a(n) = (a(n-1) + 4) mod n + 1 if n>1, a(1) = 1.

%e a(7) = 6: (^1,2,3,4,5,6,7) -> (1,2,3,4,^6,7) -> (1,2,^4,6,7) -> (1,^4,6,7) -> (1,^6,7) -> (^1,6) -> (^6).

%e a(14) = 11 => a(15) = (a(14)+4) mod 15 + 1 = 1.

%p a:= proc(n) option remember;

%p `if` (n=1, 1, (a(n-1)+4) mod n +1)

%p end:

%p seq (a(n), n=1..100);

%t a[1] = 1; a[n_] := a[n] = Mod[a[n-1]+4, n]+1; Table[a[n], {n, 1, 80}] (* _Jean-Fran├žois Alcover_, Oct 18 2013 *)

%Y Cf. A006257, A054995, A088333.

%K nonn

%O 1,2

%A _Paul Weisenhorn_, Oct 10 2010

%E Edited by _Alois P. Heinz_, Sep 06 2011

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)