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A114342 Largest number whose base n representation does not contain any digit more than once and which is not divisible by any of its base n digits, or 0 if no such number exists. 1
0, 0, 0, 35, 577, 5909, 16331, 2053379, 42374099, 987654203, 2334368201, 736867783013, 23136292864661, 789018236128979, 1936265501684027, 1147797409030816259, 48471109094902544503, 2178347851919531380901, 5463472083532379956913, 5228356786703601108032803 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

"Enigma 1343: Digital Dividend", New Scientist, Jun 04 2005, 28.

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

There are 49 numbers whose base 4 representation does not contain repeated digits. Of these, the largest which is not divisible by any of its digits is a(4)=203_4=35_10.

Any base 3 number containing only 0's and 2's with at least one 2 is divisible by 2, while any number with a 1 is divisible by 1, so no positive integer meets the criteria in base 3. Thus a(3) = 0.

PROG

(Sage)

def A114342(n):

....dd = [0] + [2..n-1]

....for width in [1..n-1][::-1]:

........found = []

........for dc in Combinations(dd, width):

............m = sum(dc) % (n-1)

............if gcd(m, n-1) in dc: continue # rule of nines

............for p in Permutations(dc[::-1]):

................s = sum((d)*n**i for i, d in enumerate(p[::-1]))

................if not any(d != 0 and s % d == 0 for d in p): found.append(s)

................if found and width == len(dd): return s

................if found and s < max(found): break

........if found: return max(found)

....return 0 # D. S. McNeil, Oct 01 2011

CROSSREFS

Cf. A113028.

Sequence in context: A278674 A219468 A267281 * A208617 A010951 A033281

Adjacent sequences:  A114339 A114340 A114341 * A114343 A114344 A114345

KEYWORD

nonn,base

AUTHOR

Francis Carr (fcarr(AT)alum.mit.edu), Feb 08 2006

EXTENSIONS

a(12)-a(20) from Nathaniel Johnston, Sep 30 2011

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.