Counting Zeroes

Let NN be the number of 00 digits in all the integers from 00 to MM (including the initial 00). Find the [smallest] non-trivial value of M>1M > 1 where N=MN=M.

For example, for M=100M=100, N=12N=12 (because it includes the initial 0), hence NMN≠M, so that M=100M=100 wouldn't be the answer. There is [not] exactly one non-trivial MM for which this is true, other than the trivial case M=1M=1.

You may use the computer or Wolfram Alpha.

Start counting the zeroes from 00, not 11, otherwise your program (if you're using one) will be a good example of Turing's Halting Problem.

{Edit, problem correction. Others have alerted me of the existence of at least 2 other M, both larger than the one stated as the solution, that meets the condition. I stand corrected, and the problem has been re-worded to ask for the smallest such non-trivial M. I think this problem now has just become more interesting, thanks to the contributors.]


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