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A327614 Number of transfers of marbles between four sets until the first repetition. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, ...

LINKS

Table of n, a(n) for n=1..64.

EXAMPLE

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).

Sequence in context: A263828 A327577 A092961 * A177711 A115945 A084750

Adjacent sequences:  A327611 A327612 A327613 * A327615 A327616 A327617

KEYWORD

nonn

AUTHOR

Tristan Cam, Sep 19 2019

STATUS

approved

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Last modified September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)