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%I #34 Apr 20 2020 09:54:38
%S 1,1,2,3,4,5,6,7,8,9,1,1,2,3,4,5,6,7,8,9,2,2,4,6,8,1,2,4,6,8,3,3,6,9,
%T 2,5,8,2,8,4,4,4,8,2,6,2,8,6,6,8,5,5,1,5,2,1,3,5,4,2,6,6,2,8,8,3,8,8,
%U 6,2,7,7,4,2,6,5,8,8,3,8,8,8,6,8,6,4,6
%N Nonzero multiplicative digital root of n.
%C Occasionally defined with a(0) = 0.
%D Discussed Jun 15 1991 on sci.math by Mayne, Rusin, Landrum et al.
%H T. D. Noe, <a href="/A051802/b051802.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F If n == A051801(n) then n else a(A051801(n)).
%p A051801 := proc(n) local d,j: d:=convert(n,base,10): return mul(`if`(d[j]=0,1,d[j]), j=1..nops(d)): end: A051802 := proc(n) local m: if(n=0)then return 1:fi: m:=n: while(length(m)>1)do m:=A051801(m): od: return m: end: seq(A051802(n),n=0..100); # _Nathaniel Johnston_, May 04 2011
%t mdr0[n_] := NestWhile[Times @@ (IntegerDigits@# /. 0 -> 1) &, n, UnsameQ, All]; Table[ mdr0@n, {n, 0, 104}] (* _Robert G. Wilson v_, Aug 04 2006 *)
%o (Haskell)
%o a051802 = until (< 10) a051801 -- _Reinhard Zumkeller_, Nov 23 2011
%o (PARI) A051801(n)=my(v=select(k->k>1,digits(n)));prod(i=1,#v,v[i])
%o a(n)=while(n>9,n=A051801(n)); n \\ _Charles R Greathouse IV_, Nov 20 2012
%o (Python)
%o from operator import mul
%o from functools import reduce
%o def A051802(n):
%o if n == 0:
%o return 1
%o while n > 9:
%o n = reduce(mul, (int(d) for d in str(n) if d != '0'))
%o return n
%o # _Chai Wah Wu_, Aug 23 2014
%o (Scala) def zeroLessIterDigitProd(n: Int): Int = n.toString.length match {
%o case 1 => n
%o case _ => zeroLessIterDigitProd(n.toString.replace("0", "").toCharArray.map(_ - 48).scanRight(1)(_ * _).head)
%o } // Note that zeroLessIterDigitProd(0) gives 0, not 1
%o List(1) ++: (1 to 99).map(zeroLessIterDigitProd) // _Alonso del Arte_, Apr 19 2020
%Y Uses A051801.
%Y Cf. A007954.
%K nonn,easy,base,nice
%O 0,3
%A _Dan Hoey_, Dec 09 1999
%E More terms from _Robert G. Wilson v_, Aug 04 2006
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