OFFSET
1,2
COMMENTS
Arrange 1, 2, 3, ... n clockwise in a circle. Starting the count at 1, delete every k-th integer clockwise until only one remains, which is T(k,n).
The main diagonal of the array (1, 1, 2, 2, 2, 4, 5, 4, ...) is A007495.
Consecutive columns down to the main diagonal (1, 2, 1, 3, 3, 2, 4, 1, 1, 2, ...) is A032434.
Period lengths of columns (1, 2, 6, 12, 60, 60, 420, 840, ...) is A003418.
LINKS
FORMULA
T(k,1) = 1;
for n > 1: T(k,n) = ((T(k,n-1) + k - 1) mod n) + 1.
EXAMPLE
.k\n 1 2 3 4 5 6 7 8 9 10
----------------------------------
.1 | 1 2 3 4 5 6 7 8 9 10 A000027
.2 | 1 1 3 1 3 5 7 1 3 5 A006257
.3 | 1 2 2 1 4 1 4 7 1 4 A054995
.4 | 1 1 2 2 1 5 2 6 1 5 A088333
.5 | 1 2 1 2 2 1 6 3 8 3 A181281
.6 | 1 1 1 3 4 4 3 1 7 3
.7 | 1 2 3 2 4 5 5 4 2 9 A178853
.8 | 1 1 3 3 1 3 4 4 3 1 A109630
.9 | 1 2 2 3 2 5 7 8 8 7
10 | 1 1 2 4 4 2 5 7 8 8
CROSSREFS
KEYWORD
AUTHOR
William Rex Marshall, Nov 21 2011
STATUS
approved