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 A360362 #4 Feb 26 2023 20:09:17 %S A360362 1,2,3,6,9,13,20,30,46,74,106,152,242,318 %N A360362 Maximum number of moves required to reach an already visited color configuration, when applying the move described in A360360 to a deck of n colored cards. %F A360362 a(n) = A357619(n) for 1 <= n <= 8, but it seems unlikely that this holds for all n. %F A360362 a(n) <= A360360(n) + A360361(n). Equality holds (i.e., the maximum period and the maximum preperiod can be obtained with the same initial configuration) for n = 1, 2, 3, 4, 10, 12, 14, ... . %e A360362 For n = 5, the initial configuration 01102 (with the top of the deck to the left) requires 9 moves to reach an already visited configuration: 01102 -> 11020 -> 10120 -> 01210 -> 12100 -> 21010 -> 12010 -> 20101 -> 02101 -> 21010. This is the maximum for 5 cards, so a(5) = 9. %e A360362 Lexicographically first optimal initial configuration for 1 <= n <= 14: %e A360362 n a(n) configuration %e A360362 1 1 0 %e A360362 2 2 01 %e A360362 3 3 001 %e A360362 4 6 0012 %e A360362 5 9 01102 %e A360362 6 13 010012 %e A360362 7 20 0111023 %e A360362 8 30 01232213 %e A360362 9 46 012110234 %e A360362 10 74 0111234234 %e A360362 11 106 01112343324 %e A360362 12 152 011102345345 %e A360362 13 242 0122112345345 %e A360362 14 318 01112345326546 %Y A360362 Cf. A357619, A360360, A360361. %K A360362 nonn,more %O A360362 1,2 %A A360362 _Pontus von Brömssen_, Feb 04 2023