A364604 Lexicographically earliest sequence, where after every appearance, a term is banned from re-appearing for twice as long as last time; first appearance bans it for 1 term.

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

Offset

1,2

Links

Table of n, a(n) for n=1..88.

Example

a(n)   ban 1  2  3  4  5  6 ...
 1         |  |  |  |  |  |
 2         x  |  |  |  |  |
 1         |  x  |  |  |  |
 2         x  |  |  |  |  |
 3         x  x  |  |  |  |
 1         |  x  x  |  |  |
 2         x  |  |  |  |  |
 3         x  x  |  |  |  |
 4         x  x  x  |  |  |
 5         x  x  x  x  |  |
 1         |  x  |  |  x  |
 2         x  |  |  |  |  |
 3         x  x  |  |  |  |
 4         x  x  x  |  |  |
 5         x  x  x  x  |  |
 6         x  x  x  x  x  |
 4         x  x  x  |  x  x
 3         x  x  |  x  |  |
 5         x  x  x  x  |  |
 1         |  x  x  x  x  |
 .
 .
 .

Prog

(PARI) A364604(N) = {my(a=vector(N), z=1); for(s=1, N, if(a[s], next); my(m=-1); for(i=s, N, if(!a[i], a[i]=z; i+=(1<<(m++)))); z++); a}
(Python)
def A364604(N):
    a = [0]*N; z=s=0
    while(s<N):
        z+=1; m=0; i=s
        while(i<N):
            if not a[i]:
                a[i]=z; i+=2**m; m+=1
            i+=1
        s+=1
    return a

Crossrefs

Cf. A364603, A364448, A364449.

Sequence in context: A243613 A194844 A138528 * A037125 A194029 A194055

Adjacent sequences: A364601 A364602 A364603 * A364605 A364606 A364607

Keyword

nonn

Author

Rok Cestnik, Jul 29 2023

Status

approved