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A064500 Smallest number with n decimal digits such that the product of its digits equals n * the sum of its digits, or 0 if impossible. 0
1, 36, 159, 1247, 11259, 111279, 1111377, 11111388, 111111399, 1111111569, 0, 111111112378, 0, 11111111112567, 111111111112568, 1111111111114448, 0, 111111111111113469, 0, 11111111111111122566, 111111111111111112779, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Note that in any base b, in this case 10, if n has a prime factor > b, then there exists no number which satisfies the criteria. Proof if (a+b+c+ ... +k)*11 = a*b*c* ... *k then this implies that z*11 = a*...*k or that there is a digit that equals 11, but this is impossible in base 10.

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

a(3) = 159 because 1*5*9 = 45 = 3*(1+5+9).

MATHEMATICA

Do[ If[n != 1 && Transpose[ FactorInteger[n]][[1, -1]] <= 10, k = (10^n - 1)/9; While[d = IntegerDigits[k]; k < 10^n && n*Apply[Plus, d] != Apply[Times, d], k++ ]; If[k < 10^n, Print[k]], If[n == 1, Print[1], Print[0]]], {n, 1, 30} ]

CROSSREFS

Sequence in context: A211759 A064244 A280397 * A264474 A268905 A017054

Adjacent sequences:  A064497 A064498 A064499 * A064501 A064502 A064503

KEYWORD

base,nonn

AUTHOR

Robert G. Wilson v, Oct 05 2001

STATUS

approved

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Last modified July 17 02:52 EDT 2019. Contains 325092 sequences. (Running on oeis4.)