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 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 k-th 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 William Rex Marshall, Rows n = 1..10, flattened Index entries for sequences related to the Josephus Problem FORMULA T(1,1) = 1; 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. 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 Cf. A003418, A007495, A032434, A198788, A198789. Sequence in context: A241534 A337137 A035050 * A306995 A212907 A308584 Adjacent sequences: A198787 A198788 A198789 * A198791 A198792 A198793 KEYWORD nonn,easy,tabf AUTHOR William Rex Marshall, Nov 21 2011 STATUS approved

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Last modified July 19 15:48 EDT 2024. Contains 374410 sequences. (Running on oeis4.)