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 A031347 Multiplicative digital root of n (keep multiplying digits of n until reaching a single digit). 52
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 3, 6, 9, 2, 5, 8, 2, 8, 4, 0, 4, 8, 2, 6, 0, 8, 6, 6, 8, 0, 5, 0, 5, 0, 0, 0, 5, 0, 0, 0, 6, 2, 8, 8, 0, 8, 8, 6, 0, 0, 7, 4, 2, 6, 5, 8, 8, 0, 8, 0, 8, 6, 8, 6, 0, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = 0 for almost all n. - Charles R Greathouse IV, Oct 02 2013 More precisely, a(n) = 0 asymptotically almost surely, namely, among others, for all numbers n which have a digit '0', and as n has more and more digits, it becomes increasingly less probable that no digit is equal to zero. (The set A011540 has density 1.) Thus the density of numbers for which a(n) > 0 is zero, although this happens for infinitely many numbers, for example all repunits n = (10^k-1)/9 = A002275(k). - M. F. Hasler, Oct 11 2015 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Multiplicative Digital Root. FORMULA a(n) = d in {1,...,9} if (but not only if) n = (10^k-1)/9 + (d-1)*10^m = A002275(k) + (d-1)*A011557(m) for some k > m >= 0. - M. F. Hasler, Oct 11 2015 MAPLE A007954 := proc(n) return mul(d, d=convert(n, base, 10)): end: A031347 := proc(n) local m: m:=n: while(length(m)>1)do m:=A007954(m): od: return m: end: seq(A031347(n), n=0..100); # Nathaniel Johnston, May 04 2011 MATHEMATICA mdr[n_] := NestWhile[Times @@ IntegerDigits@# &, n, UnsameQ, All]; Table[ mdr[n], {n, 0, 104}] (* Robert G. Wilson v, Aug 04 2006 *) Table[NestWhile[Times@@IntegerDigits[#]&, n, #>9&], {n, 0, 90}] (* Harvey P. Dale, Mar 10 2019 *) PROG (PARI) A031347(n)=local(resul); if(n<10, return(n) ); resul = n % 10; n = (n - n%10)/10; while( n > 0, resul *= n %10; n = (n - n%10)/10; ); return(A031347(resul)) for(n=1, 80, print1(A031347(n), ", ")) \\ R. J. Mathar, May 23 2006 (PARI) A031347(n)={while(n>9, n=prod(i=1, #n=digits(n), n[i])); n} \\ M. F. Hasler, Dec 07 2014 (Haskell) a031347 = until (< 10) a007954 -- Reinhard Zumkeller, Oct 17 2011, Sep 22 2011 (Python) from operator import mul from functools import reduce def A031347(n):     while n > 9:        n = reduce(mul, (int(d) for d in str(n)))     return n # Chai Wah Wu, Aug 23 2014 CROSSREFS Cf. A007954, A007953, A003001, A010888 (additive digital root of n), A031286 (additive persistence of n), A031346 (multiplicative persistence of n). Numbers having multiplicative digital roots 0-9: A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056. Sequence in context: A175421 A175420 A062078 * A087471 A128212 A187844 Adjacent sequences:  A031344 A031345 A031346 * A031348 A031349 A031350 KEYWORD nonn,base,easy,nice AUTHOR STATUS approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)