Help defining a new sequence based on decimal concatenation

[Ali Sada]

Hi everyone,

 

Hope all is well. I need help defining the following sequence and determining whether the idea is suitable for the OEIS.

 

For each positive integer n, let a(n) be the minimum number of nonnegative integers (suffixes) needed so that, for every positive integer m, at least one of those suffixes can be appended to the decimal representation of m to produce a multiple of n. We must prioritize the shortest possible suffix lengths. 

For example, when n=8, we need 4 suffixes: 6,4,2,0

1 → 16

2 → 24

3 → 32

4 → 40

(We cannot use the suffix 160 as one solution for all numbers since shorter suffixes exist.)

 

When n=14, seven suffixes are needed: 4,8,22,2,6,16,0

1 → 14

2 → 28

3 → 322

4 → 42

5 → 56

6 → 616

7 → 70

 

The first terms of the sequence are

 

0, 1, 2, 2, 1, 3, 6, 4, 8, 1, 10, 6, 12, 7, 3, ...

Best,

Ali