A209258 The original Josephus problem: 41 soldiers are arranged in a ring, and every third man is killed by his neighbor, until only the last person remains, who would kill himself. Sequence shows soldier killing order.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 1, 5, 10, 14, 19, 23, 28, 32, 37, 41, 7, 13, 20, 26, 34, 40, 8, 17, 29, 38, 11, 25, 2, 22, 4, 35, 16, 31

Offset: 1

Author

Arkadiusz Wesolowski, Jan 14 2013

Keywords

• easy
• fini
• full
• nonn

Comments

Josephus and another soldier did not agree with that proposal. By choosing positions 31 and 16 in the ring, Josephus and his companion saved their lives.

As a mathematics problem, the classic "Josephus problem" assumes that the soldiers arranged themselves in a circle and counted by threes to determine the order in which they would be killed, and the comment above assumes that Josephus and the one other survivor deliberately placed themselves in the two positions that would make them the last two survivors, but neither of these assumptions is supported by the account of Josephus himself (see the quote at the Links entry). - Jon E. Schoenfield, Jun 04 2017

Links

• Wikipedia, Josephus problem.
• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A054995.

Programs

Mathematica

Needs["Combinatorica`"]
InversePermutation@Josephus[41, 3]
lst = {}; r = 41; s = Range[r]; Do[s = RotateLeft[s, 2]; AppendTo[lst, First[s]]; s = Rest[s], {r}]; lst