A327614 Number of transfers of marbles between four sets until the first repetition.

4, 5, 10, 11, 12, 12, 12, 10, 15, 17, 12, 12, 12, 15, 17, 16, 16, 15, 19, 17, 17, 15, 15, 19, 22, 17, 16, 15, 19, 22, 21, 19, 19, 24, 26, 21, 19, 19, 24, 26, 21, 19, 19, 24, 26, 21, 19, 23, 28, 26, 21, 19, 23, 28, 26, 21, 19, 23, 28, 26, 21, 19, 23, 28

Offset: 1

Author

Tristan Cam, Sep 19 2019

Keywords

• nonn

Comments

There are initially n marbles in each of the four 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 D), (D 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, 4, 5, 9, 10, 19, 25, 34, 35, 49, 105, 194, 330, 334, 480, 1553, 1780, 2834, 2870, 4079, ...

Examples

			For n = 2, (SetA ; SetB ; SetC ; SetD):
(2 ; 2 ; 2 ; 2), ceiling(2/2)=1 marble get transferred from SetA to SetB,
(1 ; 3 ; 2 ; 2), ceiling(3/2)=2 marbles get transferred from SetB to SetC,
(1 ; 1 ; 4 ; 2), ceiling(4/2)=2 marbles get transferred from SetC to SetD,
(1 ; 1 ; 2 ; 4), ceiling(4/2)=2 marbles get transferred from SetD to SetA,
(3 ; 1 ; 2 ; 2), ceiling(3/2)=2 marbles get transferred from SetA to SetB,
(1 ; 3 ; 2 ; 2), this is a repetition, it took 5 steps to get there, so a(2) = 5.
For n = 4, (SetA ; SetB ; SetC ; SetD):
(4 ; 4 ; 4 ; 4), (2 ; 6 ; 4 ; 4), (2 ; 3 ; 7 ;4), (2 ; 3 ; 3 ; 8), (6 ; 3 ; 3 ; 4), (3 ; 6 ; 3 ; 4), (3 ; 3 ; 6 ; 4), (3 ; 3 ; 3 ; 7), (7 ; 3 ; 3 ; 3), (3 ; 7 ; 3 ; 3), (3 ; 3 ; 7 ; 3), (3 ; 3 ; 3 ; 7) which is a repetition, so a(4) = 11.
		

Crossrefs

Cf. A327565 (two sets), A327613 (three sets).