MathDB

A base 10 over-expansion of a positive integer

N

is an expression of the form

N=d_k10^k+d_{k-1}10^{k-1}+\cdots+d_0 10^0

with

d_k\ne 0

and

d_i\in\{0,1,2,\dots,10\}

for all

i.

For instance, the integer

N=10

has two base 10 over-expansions:

10=10\cdot 10^0

and the usual base 10 expansion

10=1\cdot 10^1+0\cdot 10^0.

Which positive integers have a unique base 10 over-expansion?

Problem Statement