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A364449
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Lexicographically earliest sequence where n is banned for n^3 terms after each appearance.
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4
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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, 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, 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
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OFFSET
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1,2
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COMMENTS
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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...
If banning for n terms (A364447), or n^2 terms (A364448), the sequence is eventually periodic.
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LINKS
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EXAMPLE
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a(n) ban 1 2 3 4 5 6 7 ...
1 | | | | | | |
2 x | | | | | |
1 | x | | | | |
3 x x | | | | |
1 | x x | | | |
4 x x x | | | |
1 | x x x | | |
5 x x x x | | |
1 | x x x x | |
6 x x x x x | |
1 | | x x x x |
2 x | x x x x |
1 | x x x x x |
7 x x x x x x |
1 | x x x x x x
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PROG
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(Python)
a = []
ban = [0 for n in range(500)]
for i in range(1000):
can = ban.index(0, 1)
ban = [max(b-1, 0) for b in ban]
a.append(can)
ban[can] = can**3
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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