The multiplicative digital root (MDR) and multiplicative persistence (MP) of a number, 



n


{\displaystyle n}

, is calculated rather like the Digital root except digits are multiplied instead of being added:

 Set 



m


{\displaystyle m}

 to 



n


{\displaystyle n}

 and 



i


{\displaystyle i}

 to 



0


{\displaystyle 0}

.
 While 



m


{\displaystyle m}

 has more than one digit:
 Find a replacement 



m


{\displaystyle m}

 as the multiplication of the digits of the current value of 



m


{\displaystyle m}

.
 Increment 



i


{\displaystyle i}

.
 Return 



i


{\displaystyle i}

 (= MP) and 



m


{\displaystyle m}

 (= MDR)


Task

 Tabulate the MP and MDR of the numbers 123321, 7739, 893, 899998
 Tabulate MDR versus the first five numbers having that MDR, something like:
MDR: [n0..n4]
===  ========
  0: [0, 10, 20, 25, 30]
  1: [1, 11, 111, 1111, 11111]
  2: [2, 12, 21, 26, 34]
  3: [3, 13, 31, 113, 131]
  4: [4, 14, 22, 27, 39]
  5: [5, 15, 35, 51, 53]
  6: [6, 16, 23, 28, 32]
  7: [7, 17, 71, 117, 171]
  8: [8, 18, 24, 29, 36]
  9: [9, 19, 33, 91, 119]

Show all output on this page.

Similar

The Product of decimal digits of n page was redirected here, and had the following description


Find the product of the decimal digits of a positive integer   n,   where n <= 100

The three existing entries for Phix, REXX, and Ring have been moved here, under ===Similar=== headings, feel free to match or ignore them.



References

 Multiplicative Digital Root on Wolfram Mathworld.
 Multiplicative digital root on The On-Line Encyclopedia of Integer Sequences.
 What's special about 277777788888899? - Numberphile video


F mdroot(n)
   V count = 0
   V mdr = n
   L mdr > 9
      V m = mdr
      V digits_mul = 1
      L m != 0
         digits_mul *= m % 10
         m = m I/ 10
      mdr = digits_mul
      count++
   R (count, mdr)
 
print(‘Number: (MP, MDR)’)
print(‘======  =========’)
L(n) (123321, 7739, 893, 899998)
   print(‘#6: ’.format(n), end' ‘’)
   print(mdroot(n))
 
[[Int]] table
table.resize(10)
V n = 0
L min(table.map(row -> row.len)) < 5
   table[mdroot(n)[1]].append(n)
   n++
 
print(‘’)
print(‘MP: [n0..n4]’)
print(‘==  ========’)
L(val) table
   print(‘#2: ’.format(L.index), end' ‘’)
   print(val[0.<5])