cp's OEIS Frontend

A364449 Lexicographically earliest sequence where n is banned for n^3 terms after each appearance.

%I A364449 #17 Jul 29 2023 07:03:36
%S A364449 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 A364449 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 A364449 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 A364449 Lexicographically earliest sequence where n is banned for n^3 terms after each appearance.
%C A364449 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 A364449 If banning for n terms (A364447), or n^2 terms (A364448), the sequence is eventually periodic.
%e A364449 a(n)   ban 1  2  3  4  5  6  7  ...
%e A364449  1         |  |  |  |  |  |  |
%e A364449  2         x  |  |  |  |  |  |
%e A364449  1         |  x  |  |  |  |  |
%e A364449  3         x  x  |  |  |  |  |
%e A364449  1         |  x  x  |  |  |  |
%e A364449  4         x  x  x  |  |  |  |
%e A364449  1         |  x  x  x  |  |  |
%e A364449  5         x  x  x  x  |  |  |
%e A364449  1         |  x  x  x  x  |  |
%e A364449  6         x  x  x  x  x  |  |
%e A364449  1         |  |  x  x  x  x  |
%e A364449  2         x  |  x  x  x  x  |
%e A364449  1         |  x  x  x  x  x  |
%e A364449  7         x  x  x  x  x  x  |
%e A364449  1         |  x  x  x  x  x  x
%e A364449  .
%e A364449  .
%e A364449  .
%o A364449 (Python)
%o A364449 a = []
%o A364449 ban = [0 for n in range(500)]
%o A364449 for i in range(1000):
%o A364449     can = ban.index(0,1)
%o A364449     ban = [max(b-1,0) for b in ban]
%o A364449     a.append(can)
%o A364449     ban[can] = can**3
%Y A364449 Cf. A364447, A364448, A339606.
%K A364449 nonn
%O A364449 1,2
%A A364449 _Rok Cestnik_, Jul 25 2023