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

Author

Rok Cestnik, Jul 25 2023

Keywords

• nonn
• look

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.

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  |  |  |
 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  |
 .
 .
 .
		

Links

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

Crossrefs

Cf. A364447, A364449, A028920.

Programs

C

#include
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;
}

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

Formula

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