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

1,2

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.

Links

Table of n, a(n) for n=1..90.

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

Cf. A364447, A364448, A339606.

Sequence in context: A077610 A329534 A317746 * A228179 A322313 A322315

Adjacent sequences: A364446 A364447 A364448 * A364450 A364451 A364452

Keyword

nonn

Author

Rok Cestnik, Jul 25 2023

Status

approved