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 A109783 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. 3
 2, 6, 7, 10, 11, 18, 17, 22, 25, 26, 28, 35, 39, 38, 39, 45, 48, 48, 52, 53, 56, 58, 61, 65, 67, 69, 73, 75, 79, 83, 83 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Length of the largest polydivisible number in base n. LINKS A. Mihailovs, Ponder This. Wikipedia, Polydivisible number. 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) ). [Max Alekseyev, Sep 19 2009] 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. MAPLE a:=seq(nops(convert(A109032[i], base, i+1)), i=1..nops(A109032)); # Martin Renner, Apr 05 2016 CROSSREFS Cf. A109032. Sequence in context: A341437 A327985 A189465 * A186888 A179883 A179303 Adjacent sequences:  A109780 A109781 A109782 * A109784 A109785 A109786 KEYWORD base,more,nonn AUTHOR Alec Mihailovs (alec(AT)mihailovs.com), Aug 13 2005 EXTENSIONS a(24)-a(32) from Karl W. Heuer, Jan 08 2015 STATUS approved

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Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)