Let S(x) denote the member of the sequence with x 1s. (x starts at 0)
If x mod 3 = 1 then S(x) is a multiple of 3.
If x mod 3 = 2 then S(x) is a multiple of 37.
If x mod 3 = 0 then S(x) is a multiple of 2333...3 where the number of 3s is equal to x.

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