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For some nnn and kkk let a1,a2,...,ana_{1}, a_{2}, ..., a_{n}a1,a2,...,an be a sequence where:
aia_{i}ai is a positive integer
a1=ka_{1} = ka1=k
ai+1=2×aia_{i+1} = 2 \times a_{i}ai+1=2×ai
Digit sums of all aia_{i }ai are equal (base 101010)
Can we construct such sequence for any positive integer nnn (kkk is of your choice)?
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