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

1,2

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

Table of n, a(n) for n=1..30.

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.

Crossrefs

Sequence in context: A219278 A099419 A061871 * A333216 A303669 A084651

Adjacent sequences: A182456 A182457 A182458 * A182460 A182461 A182462

Keyword

nonn

Author

Dan Fodor, Apr 30 2012

Extensions

Name corrected by Hugo Pfoertner, Oct 23 2023

Status

approved