A182459 a(n) is the number of initial persons such that the n-th person survives in the duck-duck-goose game.

1, 2, 13, 20, 46, 157, 236, 532, 1198, 4045, 6068, 13654, 46084, 103690, 1181101, 1771652, 3986218, 102162424, 229865455, 344798183, 517197275, 775795913, 1163693870, 3927466813, 5891200220, 13255200496, 29824201117, 44736301676, 100656678772, 226477527238

Offset: 1

Author

Dan Fodor, Apr 30 2012

Keywords

• nonn

Comments

In more detail: k students are sitting in a circle. A professor starts tagging them in the pattern - duck, duck, goose, ... . If a student is tagged goose he or she leaves the circle immediately. The last remaining student is the winner. These are the numbers k of initial students such that the n-th student will be the winner.

Links

• Yunier Bello Cruz and Roy Quintero-Contreras, On the Recurrence Formula for Fixed Points of the Josephus Function, arXiv:2310.12984 [math.CO], 2023. See Table 1 p. 5.
• Eric Weisstein's World of Mathematics, Josephus Problem
• Wikipedia, Josephus problem
• Index entries for sequences related to the Josephus Problem

Formula

a(n) = A081615(n)-1.

Extensions

Name corrected by Hugo Pfoertner, Oct 23 2023