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 A113028 a(n) is the largest integer whose base n digits are all different that is divisible by each of its individual digits. 3

%I #33 May 08 2024 14:49:33

%S 1,2,54,108,152,16200,2042460,4416720,9867312,2334364200,421877610,

%T 1779700673520,4025593863720,8605596007008,1147797065081426760,

%U 2851241701975626960,6723295828605676320,5463472083393768444000,32677216797923569872,29966837620559153371200

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

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

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

%H Jes Wolfe, <a href="/A113028/b113028.txt">Table of n, a(n) for n = 2..48</a>

%H Michael S. Branicky, <a href="/A113028/a113028.py.txt">Python program</a>

%H Jes Wolfe, <a href="/A113028/a113028.txt">Even faster python program</a>

%e a(2) = 1 trivially because that is the only number in base 2 that does not contain 0.

%e 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.

%o (Python) # see link for a faster version

%o from itertools import permutations

%o def fromdigits(d, b):

%o n = 0

%o for di in d: n *= b; n += di

%o return n

%o def a(n):

%o for digits in range(n-1, 0, -1):

%o for p in permutations(range(n-1, 0, -1), r=digits):

%o t = fromdigits(p, n)

%o if all(t%di == 0 for di in p):

%o return t

%o print([a(n) for n in range(2, 11)]) # _Michael S. Branicky_, Jan 17 2022

%K nonn,base

%O 2,2

%A _Peter Boothe_, Jan 03 2006

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

%E a(14) from _Michael S. Branicky_, Jan 17 2022

%E a(15)-a(17) from _Michael S. Branicky_, Jan 20 2022

%E a(18)-a(21) from _Jes Wolfe_, Apr 26 2024

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Last modified August 6 15:42 EDT 2024. Contains 374974 sequences. (Running on oeis4.)