

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), 1819.


LINKS

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


FORMULA

a(n) = (a(n1) + 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(n1)+4) mod n +1)
end:
seq (a(n), n=1..100);


MATHEMATICA

a[1] = 1; a[n_] := a[n] = Mod[a[n1]+4, n]+1; Table[a[n], {n, 1, 80}] (* JeanFrançois 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



