Sequence with equal digit sums
Number Theory
Level
2
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)?
by
Robert Szafarczyk