A364448 Lexicographically earliest sequence where n is banned for n^2 terms after each appearance.

1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 1, 6, 1, 2, 1, 3, 1, 7, 1, 2, 1, 8, 1, 4, 1, 2, 1, 3, 1, 9, 1, 2, 1, 10, 1, 5, 1, 2, 1, 3, 1, 4, 1, 2, 1, 11, 1, 12, 1, 2, 1, 3, 1, 6, 1, 2, 1, 13, 1, 4, 1, 2, 1, 3, 1, 5, 1, 2, 1, 7, 1, 14, 1, 2, 1, 3, 1, 4, 1, 2, 1, 15, 1, 16, 1, 2, 1, 3, 1, 8, 1, 2, 1, 5, 1, 4

Offset

1,2

Comments

After 12427560 terms the sequence is periodic with period 2985984. The largest periodic term is 158.

The largest term is 159 which appears only 3 times: a(4942686), a(7756992) and a(9818928).

If banning for n terms the sequence just repeats [1,2,1,3] (A364447). If banning for n^3 terms the sequence continues growing forever (A364449).

The first 41 terms are shared with A028920.

Links

Rok Cestnik, Table of n, a(n) for n = 1..10000

Formula

a(n) = a(n-2985984) for n >= 15413545.

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  |  |  |
 2         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  |
 1         |  x  |  x  x  x  |
 3         x  x  |  x  x  x  |
 1         |  x  x  x  x  x  |
 7         x  x  x  x  x  x  |
 .
 .
 .

Prog

(Python)
a = []
ban = [0 for n in range(160)]
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**2
(C)
#include<stdlib.h>
int main(void){
    int N = 1000;
    int *a = (int*)malloc((N+1)*sizeof(int));
    int *ban = (int*)malloc(160*sizeof(int));
    for(int n = 0; n < N; ++n){
        for(int can = 1; can < 160; ++can){
            if(ban[can] == 0){
                a[n] = can;
                ban[can] = can*can+1;
                break;
            }
        }
        for(int can = 1; can < 160; ++can) if(ban[can]) --ban[can];
    }
    free(a); free(ban);
    return 0;
}

Crossrefs

Cf. A364447, A364449, A028920.

Sequence in context: A087267 A128267 A289508 * A028920 A260738 A055396

Adjacent sequences: A364445 A364446 A364447 * A364449 A364450 A364451

Keyword

nonn,look

Author

Rok Cestnik, Jul 25 2023

Status

approved