%I #33 Jul 31 2023 10:09:41
%S 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,
%T 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,
%U 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
%N Lexicographically earliest sequence where n is banned for n^2 terms after each appearance.
%C After 12427560 terms the sequence is periodic with period 2985984. The largest periodic term is 158.
%C The largest term is 159 which appears only 3 times: a(4942686), a(7756992) and a(9818928).
%C 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).
%C The first 41 terms are shared with A028920.
%H Rok Cestnik, <a href="/A364448/b364448.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = a(n-2985984) for n >= 15413545.
%e a(n) ban 1 2 3 4 5 6 7 ...
%e 1 | | | | | | |
%e 2 x | | | | | |
%e 1 | x | | | | |
%e 3 x x | | | | |
%e 1 | x x | | | |
%e 4 x x x | | | |
%e 1 | | x x | | |
%e 2 x | x x | | |
%e 1 | x x x | | |
%e 5 x x x x | | |
%e 1 | x x x x | |
%e 6 x x x x x | |
%e 1 | | x x x x |
%e 2 x | | x x x |
%e 1 | x | x x x |
%e 3 x x | x x x |
%e 1 | x x x x x |
%e 7 x x x x x x |
%e .
%e .
%e .
%o (Python)
%o a = []
%o ban = [0 for n in range(160)]
%o for i in range(1000):
%o can = ban.index(0,1)
%o ban = [max(b-1,0) for b in ban]
%o a.append(can)
%o ban[can] = can**2
%o (C)
%o #include<stdlib.h>
%o int main(void){
%o int N = 1000;
%o int *a = (int*)malloc((N+1)*sizeof(int));
%o int *ban = (int*)malloc(160*sizeof(int));
%o for(int n = 0; n < N; ++n){
%o for(int can = 1; can < 160; ++can){
%o if(ban[can] == 0){
%o a[n] = can;
%o ban[can] = can*can+1;
%o break;
%o }
%o }
%o for(int can = 1; can < 160; ++can) if(ban[can]) --ban[can];
%o }
%o free(a); free(ban);
%o return 0;
%o }
%Y Cf. A364447, A364449, A028920.
%K nonn,look
%O 1,2
%A _Rok Cestnik_, Jul 25 2023