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A330930
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Starts of runs of 7 consecutive Niven (or Harshad) numbers (A005349).
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8
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1, 2, 3, 4, 10000095, 41441420, 124324220, 124324221, 124324222, 207207020, 233735070, 331531220, 350602590, 409036350, 414414020, 467470110, 621621020, 621621021, 621621022, 1030302012, 1036035020, 1051807710, 1201800620, 1243242020, 1243242021, 1243242022
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OFFSET
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1,2
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COMMENTS
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Cooper and Kennedy proved that there are infinitely many runs of 20 consecutive Niven numbers. Therefore this sequence is infinite.
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REFERENCES
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Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 36, entry 110.
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LINKS
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EXAMPLE
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10000095 is a term since 10000095 is divisible by 1 + 0 + 0 + 0 + 0 + 0 + 9 + 5 = 15, 10000096 is divisible by 16, ..., and 10000101 is divisible by 3.
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MATHEMATICA
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nivenQ[n_] := Divisible[n, Total @ IntegerDigits[n]]; niv = nivenQ /@ Range[7]; seq = {}; Do[niv = Join[Rest[niv], {nivenQ[k]}]; If[And @@ niv, AppendTo[seq, k - 6]], {k, 7, 10^7}]; seq
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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