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Lexicographically earliest sequence where n is banned for n^3 terms after each appearance.
4

%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