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%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
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