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.

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, 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, 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

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..80.

Index entries for sequences related to the Josephus Problem

Formula

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

Example

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

Maple

a:= proc(n) option remember;
      `if` (n=1, 1, (a(n-1)+4) mod n +1)
    end:
seq (a(n), n=1..100);

Mathematica

a[1] = 1; a[n_] := a[n] = Mod[a[n-1]+4, n]+1; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Oct 18 2013 *)

Crossrefs

Cf. A006257, A054995, A088333.

Sequence in context: A173410 A166548 A273138 * A171683 A249130 A134997

Adjacent sequences: A181278 A181279 A181280 * A181282 A181283 A181284

Keyword

nonn

Author

Paul Weisenhorn, Oct 10 2010

Extensions

Edited by Alois P. Heinz, Sep 06 2011

Status

approved