

A198790


Irregular table T(n,k) read by rows: Last survivor positions in Josephus problem for n numbers and a count of k, n >= 1, lcm(1, 2, 3, ..., n) >= k >= 1.


3



1, 2, 1, 3, 3, 2, 2, 1, 1, 4, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 1, 5, 3, 4, 1, 2, 4, 4, 1, 2, 4, 5, 3, 2, 5, 1, 3, 4, 1, 1, 3, 4, 1, 2, 5, 4, 2, 3, 5, 1, 3, 3, 5, 1, 3, 4, 2, 1, 4, 5, 2, 3, 5, 5, 2, 3, 5, 1, 4, 3, 1, 2, 4, 5, 2, 2, 4, 5, 2, 3, 1, 6, 5, 1, 5, 1, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Arrange 1, 2, 3, ... n clockwise in a circle. Starting the count at 1, delete every kth integer clockwise until only one remains, which is T(n,k).
In the full table in A198789, row n repeats with a periodicity of lcm(1, 2, 3, ..., n) = A003418(n). This sequence is a scan of each row in A198789 for exactly one period length.


LINKS



FORMULA

T(1,1) = 1;
for n >= 2, lcm(1, 2, ... n) >= k >=1: T(n,k) = ((T(n1,((k1) mod lcm(1, 2, ... n1)) + 1) + k  1) mod n) + 1.


EXAMPLE

n\k 1 2 3 4 5 6 7 8 9 10 11 12

1  1
2  2 1
3  3 3 2 2 1 1
4  4 1 1 2 2 3 2 3 3 4 4 1


CROSSREFS



KEYWORD

nonn,easy,tabf


AUTHOR



STATUS

approved



