A327613 Number of transfers of marbles between three sets until the first repetition.

3, 4, 8, 6, 6, 6, 8, 9, 9, 8, 11, 9, 9, 8, 11, 13, 12, 9, 11, 13, 12, 9, 11, 13, 12, 11, 14, 13, 12, 11, 14, 13, 12, 11, 14, 13, 12, 11, 14, 16, 12, 11, 14, 16, 12, 11, 14, 13, 12, 14, 14, 13, 12, 14, 14, 16, 12, 14, 14, 16, 12, 14, 14, 16, 14, 14, 14, 16, 14, 14

Offset

1,1

Comments

There are initially n marbles in each of the three sets. In the first turn, half of the marbles of set A are transferred to set B, rounding to the upper integer when halving. In the second turn, half of the marbles of set B are transferred to set C, following the same rule. The game goes on back on following the pattern (A to B), (B to C), (C to A) etc. until we reach a distribution already encountered.

a(n) is then the number of steps until the first repetition occurs.

The indexes of the maximal values are 1, 2, 3, 8, 11, 16, 27, 40, 83, 176, 179, 528, 907, 1256, 2379, 3408, ...

Links

Table of n, a(n) for n=1..70.

Example

For n = 2, (SetA ; SetB ; SetC):
(2 ; 2 ; 2), ceiling(2/2)=1 marble get transferred from SetA to SetB,
(1 ; 3 ; 2), ceiling(3/2)=2 marbles get transferred from SetB to SetC,
(1 ; 1 ; 4), ceiling(4/2)=2 marbles get transferred from SetC to SetA,
(3 ; 1 ; 2), ceiling(3/2)=2 marbles get transferred from SetA to SetB,
(1 ; 3 ; 2), this is a repetition, it took 4 steps to get there, so a(2) = 4.
For n = 4, (SetA ; SetB ; SetC):
(4 ; 4 ; 4), (2 ; 6 ; 4), (2 ; 3 ; 7), (6 ; 3 ; 3), (3 ; 6 ; 3), (3 ; 3 ; 6), (6 ; 3 ; 3) which is a repetition, so a(4) = 6.

Crossrefs

Cf. A327565 (two sets), A327614 (four sets).

Sequence in context: A336840 A253080 A050417 * A213954 A357067 A074212

Adjacent sequences: A327610 A327611 A327612 * A327614 A327615 A327616

Keyword

nonn

Author

Tristan Cam, Sep 19 2019

Status

approved