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A109783
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a(n) is the largest possible K such that there exists a K-digit in base n integer M such that for each N=1,2,...,K, the integer given by the first N digits of M in base n is divisible by N.
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1
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2, 6, 7, 10, 11, 18, 17, 22, 25, 26, 28, 35, 39, 38, 39, 45, 48, 48, 52, 53, 56, 58
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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LINKS
| A. Mihailovs, Ponder This.
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FORMULA
| Conjecture 1. a(n) is finite for all n>1. Conjecture 2. a(n) ~ n*e.
a(n) = 1 + floor( log(A109032(n)) / log(n) ) [From Max Alekseyev (maxale(AT)gmail.com), Sep 19 2009]
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EXAMPLE
| a(10)=25 because for 25-digit number 3608528850368400786036725, 3 is divisible by 1, 36 is divisible by 2, 360 is divisible by 3, ..., 3608528850368400786036725 is divisible by 25 and there is no 26-digit number with similar properties.
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CROSSREFS
| Cf. A109032.
Sequence in context: A200926 A047277 A189465 * A186888 A179883 A179303
Adjacent sequences: A109780 A109781 A109782 * A109784 A109785 A109786
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KEYWORD
| base,more,nonn
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AUTHOR
| Alec Mihailovs (alec(AT)mihailovs.com), Aug 13 2005
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