This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A327613 #12 Oct 04 2019 08:01:05 %S A327613 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, %T A327613 12,11,14,13,12,11,14,13,12,11,14,16,12,11,14,16,12,11,14,13,12,14,14, %U A327613 13,12,14,14,16,12,14,14,16,12,14,14,16,14,14,14,16,14,14 %N A327613 Number of transfers of marbles between three sets until the first repetition. %C A327613 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. %C A327613 a(n) is then the number of steps until the first repetition occurs. %C A327613 The indexes of the maximal values are 1, 2, 3, 8, 11, 16, 27, 40, 83, 176, 179, 528, 907, 1256, 2379, 3408, ... %e A327613 For n = 2, (SetA ; SetB ; SetC): %e A327613 (2 ; 2 ; 2), ceiling(2/2)=1 marble get transferred from SetA to SetB, %e A327613 (1 ; 3 ; 2), ceiling(3/2)=2 marbles get transferred from SetB to SetC, %e A327613 (1 ; 1 ; 4), ceiling(4/2)=2 marbles get transferred from SetC to SetA, %e A327613 (3 ; 1 ; 2), ceiling(3/2)=2 marbles get transferred from SetA to SetB, %e A327613 (1 ; 3 ; 2), this is a repetition, it took 4 steps to get there, so a(2) = 4. %e A327613 For n = 4, (SetA ; SetB ; SetC): %e A327613 (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. %Y A327613 Cf. A327565 (two sets), A327614 (four sets). %K A327613 nonn %O A327613 1,1 %A A327613 _Tristan Cam_, Sep 19 2019