cp's OEIS Frontend

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

%I A327614 #9 Oct 04 2019 08:01:29
%S A327614 4,5,10,11,12,12,12,10,15,17,12,12,12,15,17,16,16,15,19,17,17,15,15,
%T A327614 19,22,17,16,15,19,22,21,19,19,24,26,21,19,19,24,26,21,19,19,24,26,21,
%U A327614 19,23,28,26,21,19,23,28,26,21,19,23,28,26,21,19,23,28
%N A327614 Number of transfers of marbles between four sets until the first repetition.
%C A327614 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.
%C A327614 a(n) is then the number of steps until the first repetition occurs.
%C A327614 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, ...
%e A327614 For n = 2, (SetA ; SetB ; SetC ; SetD):
%e A327614 (2 ; 2 ; 2 ; 2), ceiling(2/2)=1 marble get transferred from SetA to SetB,
%e A327614 (1 ; 3 ; 2 ; 2), ceiling(3/2)=2 marbles get transferred from SetB to SetC,
%e A327614 (1 ; 1 ; 4 ; 2), ceiling(4/2)=2 marbles get transferred from SetC to SetD,
%e A327614 (1 ; 1 ; 2 ; 4), ceiling(4/2)=2 marbles get transferred from SetD to SetA,
%e A327614 (3 ; 1 ; 2 ; 2), ceiling(3/2)=2 marbles get transferred from SetA to SetB,
%e A327614 (1 ; 3 ; 2 ; 2), this is a repetition, it took 5 steps to get there, so a(2) = 5.
%e A327614 For n = 4, (SetA ; SetB ; SetC ; SetD):
%e A327614 (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.
%Y A327614 Cf. A327565 (two sets), A327613 (three sets).
%K A327614 nonn
%O A327614 1,1
%A A327614 _Tristan Cam_, Sep 19 2019