Basic Examples (1) 

Compute the multiplicative persistence of 14691:

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Scope (2) 

MultiplicativePersistence threads elementwise over lists:

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Compute the multiplicative persistence of the first 100 integers (OEIS A031346):

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Properties and Relations (4) 

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

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The multiplicative 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 multiplicative persistence of testint1=1234 is equal to 2:

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The single-digit integer that marks the end of the digit multiplication process is called the multiplicative digital root and is returned by the resource function MultiplicativeDigitalRoot:

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

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Possible Issues (1) 

MultiplicativePersistence requires its input to be non-negative:

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Neat Examples (1) 

The smallest integers with multiplicative persistence equal to 0,1,2,3,4,… (OEIS A003001):

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It is known that there is no number N<10²³³ with multiplicative persistence larger than 11 (Carmody 2001).