I love the fact that you based this on a question from Answers! I kind of wanted to link back to it, but I can see that you might not want people to see your answer.
This is a short coded solution but it is not efficient. A solution that involves sorting the vector, A, uses less memory and is faster but take a couple more lines of code.
Extract leading non-zero digit
vectorization in N
Stuff the Board
Determine if input is a perfect number
06 - Matrix Equations 2
compress sequence into intervals
Find the distance between runs
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