How To Make A Million

Number Theory Level 3

$50 = ( 0 + 1) \times 7 \times 7 + 1$

To "build" a number, you are allowed to perform only two operations, either adding 1 or multiplying by 7.

Starting with zero, what is the fewest number of operations you can perform to "build" 1,000,000?

For example, 50 could be built using 4 operations: $+1\rightarrow \times 7\ \rightarrow\times 7 \rightarrow + 1$ .