A364603 Lexicographically earliest sequence where after the m-th appearance of term z, it is banned from re-appearing in the next m*z terms.

1, 2, 1, 3, 2, 1, 4, 3, 5, 1, 2, 4, 6, 7, 1, 3, 5, 2, 8, 6, 1, 4, 7, 9, 10, 3, 2, 1, 5, 8, 11, 12, 6, 9, 4, 1, 10, 2, 3, 7, 13, 14, 11, 15, 1, 5, 8, 12, 16, 17, 2, 4, 6, 9, 1, 3, 13, 10, 14, 15, 18, 7, 19, 20, 21, 1, 2, 5, 11, 16, 17, 8, 4, 12, 3, 22, 23, 1, 6, 18, 24, 9, 19, 2, 13, 20, 21, 14

Offset: 1

Author

Rok Cestnik, Jul 29 2023

Keywords

• nonn
• look

Examples

			a(n)   ban 1  2  3  4  5  6  7 ...
 1         |  |  |  |  |  |  |
 2         x  |  |  |  |  |  |
 1         |  x  |  |  |  |  |
 3         x  x  |  |  |  |  |
 2         x  |  x  |  |  |  |
 1         |  x  x  |  |  |  |
 4         x  x  x  |  |  |  |
 3         x  x  |  x  |  |  |
 5         x  x  x  x  |  |  |
 1         |  |  x  x  x  |  |
 2         x  |  x  x  x  |  |
 4         x  x  x  |  x  |  |
 6         x  x  x  x  x  |  |
 7         x  x  x  x  x  x  |
 1         |  x  |  x  |  x  x
 3         x  x  |  x  |  x  x
 5         x  x  x  x  |  x  x
 2         x  |  x  x  x  x  x
 8         x  x  x  x  x  x  x
 6         x  x  x  x  x  |  x
 1         |  x  x  |  x  x  x
 .
 .
 .
		

Links

• Rok Cestnik, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16.
• Michael De Vlieger, Plot [b(k) > n] at (x,y) = (n,k), for n = 1..2^12, where k may appear at index b(k) and brackets are Iverson. Hence if b(k) > n, k is banned and shown in black else k is permitted and shown in white. This image is similar to the Example but rotated 90 degrees counterclockwise.

Crossrefs

Cf. A364604, A364448, A364449.

Programs

Mathematica

c[] := 0; q[] := 1; r = k = 1; nn = 120; Do[Set[{a[n], c[k]}, {k, n + k*q[k] + 1}]; q[k]++; If[k > r, r = k]; k = MinimalBy[Range[r], c, 1][[1]]; If[c[k] > n + 1, k = r + 1], {n, nn}]; Array[a, nn] (* Michael De Vlieger, Aug 13 2023 *)

PARI

A364603(N) = {my(a=vector(N),z=1); for(s=1,N, if(a[s],next); my(m=0); for(i=s,N, if(!a[i], a[i]=z; i+=(z*(m++)))); z++); a}

Python

def A364603(N):
    a = [0]*N; z=s=0
    while(s