# Sequence with equal digit sums

For some $n$ and $k$ let $a_{1}, a_{2}, ..., a_{n}$ be a sequence where:

• $a_{i}$ is a positive integer

• $a_{1} = k$

• $a_{i+1} = 2 \times a_{i}$

• Digit sums of all $a_{i }$ are equal (base $10$)

Can we construct such sequence for any positive integer $n$ ($k$ is of your choice)?

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