

A225381


Elimination order of the first person in a Josephus problem.


2



1, 2, 2, 4, 3, 5, 4, 8, 5, 8, 6, 11, 7, 11, 8, 16, 9, 14, 10, 18, 11, 17, 12, 23, 13, 20, 14, 25, 15, 23, 16, 32, 17, 26, 18, 32, 19, 29, 20, 38, 21, 32, 22, 39, 23, 35, 24, 47, 25, 38, 26, 46, 27, 41, 28, 53, 29, 44, 30, 53, 31, 47, 32, 64, 33, 50, 34, 60, 35
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OFFSET

1,2


COMMENTS

In a Josephus problem such as A006257, a(n) is the order in which the person originally first in line is eliminated.
The number of remaining survivors after the person originally first in line has been eliminated, i.e., na(n), gives the fractal sequence A025480.
For the linear version, see A225489.


LINKS



FORMULA

a(n) = (n+1)/2 (odd n); a(n) = a(n/2) + n/2 (even n).


EXAMPLE

If there are 7 persons to begin with, they are eliminated in the following order: 2,4,6,1,5,3,7. So the first person (the person originally first in line) is eliminated as number 4. Therefore a(7) = 4.


MATHEMATICA

t = {1}; Do[AppendTo[t, If[OddQ[n], (n + 1)/2, t[[n/2]] + n/2]], {n, 2, 100}]; t (* T. D. Noe, May 17 2013 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



