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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

P. Weisenhorn, Josephus und seine Folgen, MNU, 59 (2006), 18-19.

LINKS

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

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-Fran├žois 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

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Last modified August 20 06:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)