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We start with a blank 1-indexed sequence:
_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,...
In the nth step, we fill in every a(n) blanks with the integers greater than 1, where a(n) is the nth entry in the sequence.
After the first step:
2,_,3,_,4,_,5,_,6,_,7,_,8,_,9,_,10,_,11,_,12,_,13,_...