%I #17 Jul 29 2023 07:03:36
%S 1,2,1,3,1,4,1,5,1,6,1,2,1,7,1,8,1,9,1,10,1,2,1,11,1,12,1,13,1,14,1,2,
%T 1,3,1,15,1,16,1,17,1,2,1,18,1,19,1,20,1,21,1,2,1,22,1,23,1,24,1,25,1,
%U 2,1,3,1,26,1,27,1,28,1,2,1,4,1,29,1,30,1,31,1,2,1,32,1,33,1,34,1,35
%N Lexicographically earliest sequence where n is banned for n^3 terms after each appearance.
%C Sequence is unbounded. The fastest branch grows asymptotically linearly: limsup a(n)/n > 1-Sum_{n>0} 1/(n^3+1) = 1-A339606 = 0.313496...
%C If banning for n terms (A364447), or n^2 terms (A364448), the sequence is eventually periodic.
%e a(n) ban 1 2 3 4 5 6 7 ...
%e 1 | | | | | | |
%e 2 x | | | | | |
%e 1 | x | | | | |
%e 3 x x | | | | |
%e 1 | x x | | | |
%e 4 x x x | | | |
%e 1 | x x x | | |
%e 5 x x x x | | |
%e 1 | x x x x | |
%e 6 x x x x x | |
%e 1 | | x x x x |
%e 2 x | x x x x |
%e 1 | x x x x x |
%e 7 x x x x x x |
%e 1 | x x x x x x
%e .
%e .
%e .
%o (Python)
%o a = []
%o ban = [0 for n in range(500)]
%o for i in range(1000):
%o can = ban.index(0,1)
%o ban = [max(b-1,0) for b in ban]
%o a.append(can)
%o ban[can] = can**3
%Y Cf. A364447, A364448, A339606.
%K nonn
%O 1,2
%A _Rok Cestnik_, Jul 25 2023