A321781 Least q > 1 letting Josephus survive if he finds himself at position j in the circle of m persons, but is allowed to name the elimination parameter q such that every q-th person is executed, written as triangle T(m,j), m > 1, j <= m.
0, 2, 3, 5, 3, 2, 2, 4, 6, 10, 4, 5, 2, 3, 11, 3, 10, 8, 6, 2, 27, 11, 4, 6, 3, 7, 5, 2, 2, 19, 5, 7, 12, 4, 3, 9, 3, 7, 2, 42, 35, 11, 6, 5, 21, 8, 19, 5, 3, 2, 15, 9, 10, 7, 12, 16, 26, 24, 40, 7, 36, 2, 5, 4, 14, 12, 4, 9, 6, 26, 8, 11, 18, 13, 2, 3, 12, 7, 21, 10, 15, 11, 4, 5, 23, 13, 6, 12, 2, 18, 3
Offset: 1
Examples
The triangle begins: 0 2 3 5 3 2 2 4 6 10 4 5 2 3 11 3 10 8 6 2 27 11 4 6 3 7 5 2 2 19 5 7 12 4 3 9 3 7 2 42 35 11 6 5 21 8 19 5 3 2 15 9 10 7 12 16 26 24 40 7 36 2 5 4 14 12 4 9 6 26 8 11 18 13 2 3 12 7 ... 3 persons: q = 2: 111 -> 101 -> 001. Position 3 survives, therefore T(3,3) = 2; q = 3: 111 -> 110 -> 010. Position 2 survives, therefore T(3,2) = 3; q = 4: 111 -> 011 -> 010. Position 2 survives, already covered by q = 3; q = 5: 111 -> 101 -> 100. Position 1 survives, therefore T(3,1) = 5.
References
- Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics, 2nd ed., Addison-Wesley, 1994, page 20.
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