Multiplicative-Persistence
Inspired from a numberphile
What is it ?
Given any positive number (n), multiply the all of the digits of the number. Repeat the process until you are left with only 1 digit. We are interested in the steps taken by the number (n) to get reduced to a digit.
- example : n = 327
- step 0 : 327
- step 1 : 3*2*7 = 42
- step 2 : 4*2 = 8
And hence n = 327 takes 2 steps. Now, we are interested in the smallest number that takes a certain given amount of steps.
Work done till now
I've successfully found out the smallest number that takes 9 steps using python.
Future work
Making the code more efficient and aiming to find out the smallest number for 12 or more steps.