Basic Examples (1) 

Find the additive persistence of 1191:

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Scope (2) 

AdditivePersistence threads elementwise over lists:

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Compute the additive persistence of the first 100 integers (OEIS A031286):

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Properties and Relations (4) 

The result returned by AdditivePersistence can be manually computed using Length with NestWhileList:

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The additive persistence of an integer can also be manually computed with no high-level functions:

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Because testint3 is a single-digit integer, the process terminates here. Since it took two steps to reach testint3, the additive persistence of testint1=1234 is equal to 2:

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The single-digit integer that marks the end of the digit addition process is called the additive digital root and is returned by the resource function AdditiveDigitalRoot:

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The multiplicative analogue of additive persistence is called multiplicative persistence and is returned by the resource function MultiplicativePersistence:

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Possible Issues (1) 

AdditivePersistence requires its input to be non-negative:

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Neat Examples (1) 

The smallest integers with additive persistence equal to 0,1,2,3,4,… (OEIS A006050):

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The smallest integer with additive persistence 5 is known to equal 1 followed by 2222222222222222222222 9’s.