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

0,3

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

Formula

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

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 *)

Prog

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

Crossrefs

Uses A051801.

Cf. A007954.

Sequence in context: A054055 A067456 A052429 * A051801 A071205 A066750

Adjacent sequences: A051799 A051800 A051801 * A051803 A051804 A051805

Keyword

nonn,easy,base,nice

Author

Dan Hoey, Dec 09 1999

Extensions

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

Status

approved