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Search: id:A126789
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| A126789 |
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a(n) is the smallest number such that the product of its digits is n times the sum of its digits, or 0 if no such number exists. |
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+0
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| 1, 36, 66, 88, 257, 268, 279, 448, 369, 459, 0, 666, 0, 578, 579, 678, 0, 1689, 0, 2558, 789, 0, 0, 1899, 13557, 0, 999, 3477, 0, 2589, 0, 2688, 0, 0, 13578, 3489, 0, 0, 0, 3588, 0, 2799, 0, 0, 4569, 0, 0, 4668, 4677, 5568, 0, 0, 0, 3699, 0, 3789, 0, 0, 0, 4599, 0, 0
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(11) = 0. Proof: 11 is a prime number and the product of digits of a number in base 10 can never be a multiple of 11. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 07 2007
More generally, a(n) = 0 for all n which are divisible by a prime bigger than 7. This means that the sequence will almost always be 0 (with the set of exceptions having density 0). In each term the digits will be increasing (otherwise we could rearrange the digits so that they form a smaller number with the requested property). If all prime factors of n do not exceed 7, does this mean that the a(n) is not 0? - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 14 2007
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EXAMPLE
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a(2)=36 because 3*6/(3+6)=2 and no number smaller than 36 has this property.
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MAPLE
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for n from 1 to 10 do b:=proc(k) local kk: kk:=convert(k, base, 10): if product(kk[j], j=1..nops(kk))=n*sum(kk[j], j=1..nops(kk)) then k else fi end: a[n]:=[seq(b(k), k=1..1000)][1]: od: seq(a[n], n=1..10); # program works only for n from 1 to 10 - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2007
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MATHEMATICA
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a[1] := 1; a[n_] := Module[{}, k = 0; If[FactorInteger[n][[ -1, 1]] < 8, k = 1; While[Times @@ IntegerDigits[k] != n*Plus @@ IntegerDigits[k], k++ ]]; k]; Table[a[i], {i, 1, 80}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 14 2007
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CROSSREFS
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This sequence is a subsequence of A061013 (Product of digits of n) is divisible by (sum of digits of n), where 0's are not permitted.
Sequence in context: A082295 A060671 A074315 this_sequence A068144 A036785 A114127
Adjacent sequences: A126786 A126787 A126788 this_sequence A126790 A126791 A126792
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KEYWORD
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base,nonn
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AUTHOR
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Tanya Khovanova (tanyakh(AT)yahoo.com), Feb 19 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2007
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 14 2007
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