A051802 Nonzero multiplicative digital root of n.

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, 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, 6, 2, 7, 7, 4, 2, 6, 5, 8, 8, 3, 8, 8, 8, 6, 8, 6, 4, 6

Offset: 0

Author

Dan Hoey, Dec 09 1999

Keywords

• nonn
• easy
• base
• nice

Comments

Occasionally defined with a(0) = 0.

References

• Discussed Jun 15 1991 on sci.math by Mayne, Rusin, Landrum et al.

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Uses A051801.

Cf. A007954.

Programs

Haskell

a051802 = until (< 10) a051801  -- Reinhard Zumkeller, Nov 23 2011

Maple

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

Mathematica

mdr0[n_] := NestWhile[Times @@ (IntegerDigits@# /. 0 -> 1) &, n, UnsameQ, All]; Table[ mdr0@n, {n, 0, 104}] (* Robert G. Wilson v, Aug 04 2006 *)

PARI

A051801(n)=my(v=select(k->k>1,digits(n)));prod(i=1,#v,v[i])
a(n)=while(n>9,n=A051801(n)); n \\ Charles R Greathouse IV, Nov 20 2012

Python

from operator import mul
from functools import reduce
def A051802(n):
    if n == 0:
        return 1
    while n > 9:
        n = reduce(mul, (int(d) for d in str(n) if d != '0'))
    return n
# Chai Wah Wu, Aug 23 2014

Scala

def zeroLessIterDigitProd(n: Int): Int = n.toString.length match {
  case 1 => n
  case  => zeroLessIterDigitProd(n.toString.replace("0", "").toCharArray.map( - 48).scanRight(1)( * ).head)
} // Note that zeroLessIterDigitProd(0) gives 0, not 1
List(1) ++: (1 to 99).map(zeroLessIterDigitProd) // Alonso del Arte, Apr 19 2020

Formula

If n == A051801(n) then n else a(A051801(n)).

Extensions

More terms from Robert G. Wilson v, Aug 04 2006