Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the multiplicative persistence, in any base, of an integer
ResourceFunction["MultiplicativePersistence"][n,b] gives the multiplicative persistence of the non-negative integer n when expressed in the base b. | |
ResourceFunction["MultiplicativePersistence"][n] gives the base-10 muliplicative persistence of n. |
Compute the multiplicative persistence of 14691:
In[1]:= | ![]() |
Out[1]= | ![]() |
Compute the multiplicative persistence of 14691, base-14:
In[2]:= | ![]() |
Out[2]= | ![]() |
MultiplicativePersistence threads elementwise over lists:
In[3]:= | ![]() |
Out[4]= | ![]() |
In[5]:= | ![]() |
Out[5]= | ![]() |
Compute the multiplicative persistence of the first 100 integers (OEIS A031346):
In[6]:= | ![]() |
Out[6]= | ![]() |
The result returned by MultiplicativePersistence can be iteratively computed using NestWhileList:
In[7]:= | ![]() |
Out[7]= | ![]() |
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:
In[8]:= | ![]() |
Out[8]= | ![]() |
In[9]:= | ![]() |
Out[9]= | ![]() |
In[10]:= | ![]() |
Out[10]= | ![]() |
The additive analogue of multiplicative persistence is called additive persistence and is returned by the resource function AdditivePersistence:
In[11]:= | ![]() |
Out[11]= | ![]() |
In[12]:= | ![]() |
Out[12]= | ![]() |
In[13]:= | ![]() |
Out[13]= | ![]() |
MultiplicativePersistence requires its input to be non-negative:
In[14]:= | ![]() |
Out[14]= | ![]() |
The smallest integers with multiplicative persistences equal to 0,1,2,3,4,… (OEIS A003001) are:
In[15]:= | ![]() |
Out[15]= | ![]() |
It is known that there is no number N<10233 with multiplicative persistence larger than 11 (Carmody 2001).
This work is licensed under a Creative Commons Attribution 4.0 International License