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Sequences of consecutive $n$-Niven numbers. (English) Zbl 0796.11002
An $n$-Niven number is a positive integer that is divisible by the sum of the digits in its base $n$ expansion. In 1992 Cooper and Kennedy showed that there does not exist a sequence of more than 20 consecutive 10-Niven numbers. This result is best possible. In the current paper the author generalizes this result by showing that for any $n\geq 2$ there does not exist a sequence of more than $2n$ consecutive $n$-Niven numbers. It is conjectured that this result is best possible for all $n\geq 2$.

11A63Radix representation; digital problems
11A07Congruences; primitive roots; residue systems
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