Problem Statement

There are several so-called "self-describing" or "self-descriptive" integers. An integer is said to be "self-describing" if it has the property that, when digit positions are labeled 0 to N-1, the digit in each position is equal to the number of times that that digit appears in the number. For example,   2020   is a four-digit self describing number:

Self-describing numbers < 100.000.000  are:     1210,   2020,   21200,   3211000,   42101000.

Let's start with the solution:

   digits   =: 10&#.^:_1
   counts   =: _1 + [: #/.~ i.@:# , ]
   selfdesc =: = counts&.digits"0       NB.  Note use of "under"


   selfdesc 2020 1210 21200 3211000 43101000 42101000
1 1 1 1 0 1


   I.@:selfdesc i. 1e6
1210 2020 21200