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


USING: arrays formatting fry io kernel lists lists.lazy math
math.text.utils prettyprint sequences ;
IN: rosetta-code.multiplicative-digital-root
 
: mdr ( n -- {persistence,root} )
    0 swap
    [ 1 digit-groups dup length 1 > ] [ product [ 1 + ] dip ] while
    dup empty? [ drop { 0 } ] when first 2array ;
 
: print-mdr ( n -- )
    dup [ 1array ] dip mdr append
    "%-12d has multiplicative persistence %d and MDR %d.\n"
    vprintf ;
 
: first5 ( n -- seq ) ! first 5 numbers with MDR of n
    0 lfrom swap '[ mdr second _ = ] lfilter 5 swap ltake list>array ;
 
: print-first5 ( i n -- )
    "%-5d" printf bl first5 [ "%-5d " printf ] each nl ;
 
: header ( -- )
    "MDR | First five numbers with that MDR" print
    "--------------------------------------" print ;
 
: first5-table ( -- )
    header 10 iota [ print-first5 ] each-index ;
 
: main ( -- )
    { 123321 7739 893 899998 } [ print-mdr ] each nl first5-table ;
 
MAIN: main