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A053312
a(n) contains n digits (either '1' or '2') and is divisible by 2^n.
a(n)=a(n-1)+10^(n-1)*(2-[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 2, if not then n-th term begins with a 1.