Excludivisible numbers Given an integer N, output the Nth positive number K with the following property in decimal base:

For each digit I at position P of K, the number formed from K by removing the Pth digit (i.e. I) is divisible by I.

Example and remarks

324 is such a number:


3 divides 24
2 divides 34
4 divides 32


Note 1: we assume that the empty number is divisible by anything, like 0. Therefore 1, 2, 3, 4, 5, 6, 7, 8 and 9 are valid.

Note 2: K cannot contain the digit 0, since you cannot divide by 0.

Inputs and outputs


You may take the input as a function argument, through STDIN, etc.
You may return the output from a function, through STDOUT, etc.
You may index those numbers starting from 0 (in which case N &gt;= 0) or from 1 (in which case N &gt; 0), whichever suits you more.


Test cases

Those examples are indexed from 0, so if you indexed from 1, then add 1 to the numbers in the N column.

N    Output
0    1
4    5
8    9
15   77
16   88
23   155
42   742
47   1113
121  4244
144  6888
164  9999


Scoring

This is code-golf, so the shortest answer in bytes wins.
Jelly, 21 19 bytes

DLR©œ^€®ịDḌḍ@DPȧµ#Ṫ


Input is 1-indexed. Try it online!

How it works

DLR©œ^€®ịDḌḍ@DPȧµ#Ṫ  Main link. No arguments.

                µ    Convert the chain to the left into a link.
                 #   Read n from STDIN and execute the link to the left for
                     k = 0, 1, 2, ... until n value return a truthy value.
D                      Convert D to base 10 (digit array).
 LR                    Construct the range from 1 to the length of the digit array.
   ©                   Copy the range to the register.
       ®               Yield the value of the register.
    œ^€                Take the multiset difference of each element of the range
                       and the range itself.
        ịD             Index into the digit array.
          Ḍ            Convert each list of digits to integer.
                       This yields all numbers with one suppressed digit.
           ḍ@D         Test each of these numbers for divisibility by the
                       suppressed digit from the digit array.
              P        Take the product of the resulting Booleans.
               ȧ       Logical AND with k (k would return 1).
                  Ṫ  Tail; extract the last (nth) element.