mathematics - Martin Gardner - Persistence

A number's persistence is :

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  The number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number

  
  


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  Then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained.

  
  

For example : 77 has a persistence of four because it requires four steps to reduce it to one digit: 77-49-36-18-8.

The smallest number of persistence one is 10

The smallest of persistence two is 25

The smallest of persistence three is 39

The smaller of persistence four is 77

What is the smallest number of persistence five?

Answer

Brute forcing with Lua gave me

679

This is also confirmed by Wikipedia and OEIS:

http://en.m.wikipedia.org/wiki/Persistence_of_a_number

http://oeis.org/A003001