

A113028


a(n) is the largest integer whose base n digits are all different that is divisible by each of its individual digits.


3



1, 2, 54, 108, 152, 16200, 2042460, 4416720, 9867312, 2334364200, 421877610, 1779700673520, 4025593863720, 8605596007008, 1147797065081426760, 2851241701975626960, 6723295828605676320, 5463472083393768444000, 32677216797923569872, 29966837620559153371200
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OFFSET

2,2


COMMENTS

Note that this definition precludes the digit 0 appearing anywhere in the base n representation of the number.


REFERENCES

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


LINKS



EXAMPLE

a(2) = 1 trivially because that is the only number in base 2 that does not contain 0.
a(4) = 54 because in base 4, 54 is 312_4. There is only one number containing different digits and no zeros higher than that, namely 321_4, but 321_4 is not divisible by 2.


PROG

(Python) # see link for a faster version
from itertools import permutations
def fromdigits(d, b):
n = 0
for di in d: n *= b; n += di
return n
def a(n):
for digits in range(n1, 0, 1):
for p in permutations(range(n1, 0, 1), r=digits):
t = fromdigits(p, n)
if all(t%di == 0 for di in p):
return t


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS

a(11)a(13) from Francis Carr (fcarr(AT)alum.mit.edu), Feb 08 2006


STATUS

approved



