Find the value which best completes the series.
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6, 15, 41, 113, ?
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The logic is 6, 5, 4, 3 so it has to be 2. The 1s follow the Fibonacci sequence: 6 has zero 1s, 5 has one 1, 4 has one 1, 3 has two 1s so... 0, 1, 1, 2. So 2 has to have three 1s on its right — 2111.
one special digit X starts at 6 and decreases by 1 every iteration. it will also change positions in the next number.
meanwhile, the number of total digits increases by 1 TO THE LEFT when every possible position for X has been done. the digits added are always 1s.
the simplest solution is for X to be moving right only.
309 is just ok, but this one is better for the reason that it's not an arbitrary start of a hidden subsequence.