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A051802 Nonzero multiplicative digital root of n. 35
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy,base,nice
AUTHOR
Dan Hoey, Dec 09 1999
EXTENSIONS
More terms from Robert G. Wilson v, Aug 04 2006
STATUS
approved

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Last modified July 15 21:59 EDT 2024. Contains 374334 sequences. (Running on oeis4.)