A198790 - OEIS

%I #18 Jun 23 2020 05:03:31

%S 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,

%T 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,

%U 4,3,1,2,4,5,2,2,4,5,2,3,1,6,5,1,5,1,4

%N 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.

%C 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(n,k).

%C 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.

%H William Rex Marshall, <a href="/A198790/b198790.txt">Rows n = 1..10, flattened</a>

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%F T(1,1) = 1;

%F for n >= 2, lcm(1, 2, ... n) >= k >=1: T(n,k) = ((T(n-1,((k-1) mod lcm(1, 2, ... n-1)) + 1) + k - 1) mod n) + 1.

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

%e ---------------------------------------

%e 1 |  1

%e 2 |  2  1

%e 3 |  3  3  2  2  1  1

%e 4 |  4  1  1  2  2  3  2  3  3  4  4  1

%Y Cf. A003418, A007495, A032434, A198788, A198789.

%K nonn,easy,tabf

%O 1,2

%A _William Rex Marshall_, Nov 21 2011