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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
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
Sequence in context: A241534 A337137 A035050 * A306995 A212907 A308584
KEYWORD
nonn,easy,tabf
AUTHOR
STATUS
approved

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