MathDB

Source: 2018 Canadian Open Math Challenge Part B Problem 3 —--
The doubling sum function is defined by

D(a,n)=\overbrace{a+2a+4a+8a+...}^{\text{n terms}}.

For example, we have

D(5,3)=5+10+20=35

and

D(11,5)=11+22+44+88+176=341.

Determine the smallest positive integer

n

such that for every integer

i

between

1

and

6

, inclusive, there exists a positive integer

a_i

such that

D(a_i,i)=n.

Problem Statement