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A364449
Lexicographically earliest sequence where n is banned for n^3 terms after each appearance.
4
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
OFFSET
1,2
COMMENTS
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.
EXAMPLE
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
.
.
.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Rok Cestnik, Jul 25 2023
STATUS
approved