A198791 Least count k that deletes the alternate (odd) numbers in the Josephus problem for a circle of numbers 1, 2, 3, ... 2*n, leaving the even numbers undeleted.

1, 5, 19, 27, 87, 989, 3119, 5399, 8189, 99663, 57455, 222397, 2603047, 8476649, 117917347, 290190179, 360064247, 1344262919, 3181391639, 39179386959, 204692414215, 165424388219, 2254874520599, 2922139183443, 594630799853

Offset

1,2

Comments

Arrange 1, 2, 3, ... 2*n clockwise in a circle. Starting the count at 1, delete every k-th integer clockwise until exactly half of the numbers have been deleted. a(n) is the least positive integer k for which the deleted numbers are the odd numbers.

Deleting the alternate (even) numbers from a circle of 2*n numbers leaving the odd numbers is trivially achieved with k = 2 for all n >= 1.

Links

Table of n, a(n) for n=1..25.

P. Schumer, The Josephus Problem: Once More Around, Mathematics Magazine, Vol. 75:1 (2002), 12-17.

Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A198788, A198789.

Sequence in context: A018475 A119238 A218885 * A332155 A366211 A061388

Adjacent sequences: A198788 A198789 A198790 * A198792 A198793 A198794

Keyword

nonn,more

Author

William Rex Marshall, Nov 21 2011

Status

approved