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A064500
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Smallest number with n decimal digits such that the product of its digits equals n * the sum of its digits, or 0 if impossible.
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0
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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; internal format)
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OFFSET
| 1,2
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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.
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EXAMPLE
| a(3) = 159 because 1*5*9 = 45 = 3*(1+5+9)
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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} ]
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CROSSREFS
| Sequence in context: A160754 A117511 A064244 * A017054 A166708 A127657
Adjacent sequences: A064497 A064498 A064499 * A064501 A064502 A064503
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KEYWORD
| base,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 05 2001
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