How To Make A Million

Relevant wiki: Number Base - Problem Solving

Perhaps the most intuitive way to think about this question, is to consider base $7$ :

$1000000_{10} = 11333311_7$

In base $7$ , multiplying by $7$ is like shifting $1$ .

So to "build" this number, you would "make" one digit at a time, i.e. add one, shift, add $1$ , shift, add $3$ , shift, etc.

Or translated into the operations in this problem, this would be equivalent to performing the following operations in order:

$+1 \times 7 +1 \times 7 +1 +1 +1 \times 7 +1 +1 +1 \times 7 +1 +1 +1 \times 7 +1 +1 +1 \times 7 +1 \times 7 +1$

And this is $\boxed{23}$ operations.