Additive Persistence

A number’s additive persistence is the number of additions required to obtain a single digit from a number n. That last digit obtained is called the digital root.

For example, given the starting number of 9876:

9 + 8 + 7 + 6 = 30
3 + 0 = 3

We went through 2 rounds of addition, so the additive persistence is 2. The last digit obtained was 3, and thus, the digital root is 3.

Weisstein, Eric W. “Additive Persistence.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/AdditivePersistence.html

Implementation

This Python program, from a high level, does a few things:

• Accepts user input in the form of a standard integer
• Splits the input integer into a list[] of digits
• Performs the mathematics above by calculating the sum of digits, determining if there are more than one digits, and looping if so
• Returns the additive persistence of the user-provided integer