A139285 - OEIS

A139285

Smallest nontrivial number m that when expressed in base n and then interpreted in base 10, is a multiple of the original number.

3, 2, 7, 6, 5, 308, 51, 34217, 7794416

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OFFSET

1,1

COMMENTS

Not defined for n>9.

Note that for n=1, the unitary numeral system is used, whereas for n>=2, it is the usual base-dependent positional numeral system. - Michel Marcus, Sep 16 2020

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

a(1)=3 since 3 in base 1 ('unary') is 111 and, interpreted in base 10, 111 is a number divisible by 3, whereas 2 in base 1 is 11 and, interpreted in base 10, 11 is not divisible by 2.

a(3)=7 since 7 in base 3 is 21 and, interpreted in base 10, 21 is divisible by 7, whereas 3, 4, 5, 6 in base 3 are, respectively, 10, 11, 12, 20 and, interpreted in base 10, these are numbers not divisible, respectively, by 3, 4, 5, 6.

Trivial solutions (i.e., m<n for n>1 and m=n for n=1) are not considered here.

PROG

(Python)

m, M=2, 11

while M%m>0:

m, M=m+1, 10*M+1

print(1, m)

for n in range(2, 10):

m, M, d=n, 10, 10-n

while M%m>0:

m=m+1

u, s=m, 0