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%I #18 Jun 23 2020 14:34:00
%S 1,2,1,3,1,1,4,3,2,1,5,1,2,1,1,6,3,1,2,2,1,7,5,4,2,1,1,1,8,7,1,1,2,1,
%T 2,1,9,1,4,5,2,3,3,1,1,10,3,7,2,1,4,2,3,2,1,11,5,1,6,6,4,4,3,2,1,1,12,
%U 7,4,1,3,3,5,1,3,2,2,1,13,9,7,5,8,1,5,3
%N Array T(k,n) read by descending antidiagonals: Last survivor positions in Josephus problem for n numbers and a count of k, n >= 1, 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(k,n).
%C The main diagonal of the array (1, 1, 2, 2, 2, 4, 5, 4, ...) is A007495.
%C Consecutive columns down to the main diagonal (1, 2, 1, 3, 3, 2, 4, 1, 1, 2, ...) is A032434.
%C Period lengths of columns (1, 2, 6, 12, 60, 60, 420, 840, ...) is A003418.
%H William Rex Marshall, <a href="/A198788/b198788.txt">First 141 antidiagonals of array, flattened</a>
%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F T(k,1) = 1;
%F for n > 1: T(k,n) = ((T(k,n-1) + k - 1) mod n) + 1.
%e .k\n 1 2 3 4 5 6 7 8 9 10
%e ----------------------------------
%e .1 | 1 2 3 4 5 6 7 8 9 10 A000027
%e .2 | 1 1 3 1 3 5 7 1 3 5 A006257
%e .3 | 1 2 2 1 4 1 4 7 1 4 A054995
%e .4 | 1 1 2 2 1 5 2 6 1 5 A088333
%e .5 | 1 2 1 2 2 1 6 3 8 3 A181281
%e .6 | 1 1 1 3 4 4 3 1 7 3
%e .7 | 1 2 3 2 4 5 5 4 2 9 A178853
%e .8 | 1 1 3 3 1 3 4 4 3 1 A109630
%e .9 | 1 2 2 3 2 5 7 8 8 7
%e 10 | 1 1 2 4 4 2 5 7 8 8
%Y Cf. A000027 (k = 1), A006257 (k = 2), A054995 (k = 3), A088333 (k = 4), A181281 (k = 5), A178853 (k = 7), A109630 (k = 8).
%Y Cf. A003418, A007495 (main diagonal), A032434, A198789, A198790.
%K nonn,easy,tabl
%O 1,2
%A _William Rex Marshall_, Nov 21 2011
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