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

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

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

Jes Wolfe, Table of n, a(n) for n = 2..48

Michael S. Branicky, Python program

Jes Wolfe, Even faster python program

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(n-1, 0, -1):
        for p in permutations(range(n-1, 0, -1), r=digits):
            t = fromdigits(p, n)
            if all(t%di == 0 for di in p):
                return t
print([a(n) for n in range(2, 11)]) # Michael S. Branicky, Jan 17 2022

Crossrefs

Sequence in context: A083471 A078691 A280754 * A200195 A202739 A055024

Adjacent sequences: A113025 A113026 A113027 * A113029 A113030 A113031

Keyword

nonn,base

Author

Peter Boothe, Jan 03 2006

Extensions

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

a(14) from Michael S. Branicky, Jan 17 2022

a(15)-a(17) from Michael S. Branicky, Jan 20 2022

a(18)-a(21) from Jes Wolfe, Apr 26 2024

Status

approved