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

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

Author

Rok Cestnik, Jul 25 2023

Keywords

• nonn

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.

Examples

			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
 .
 .
 .
		

Crossrefs

Cf. A364447, A364448, A339606.

Programs

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