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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 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

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