The Answer Is Quite Large

Logic Level 4

On the left side of the above equation, fill in each square with a distinct digit (0 to 9), and each circle with one of the 4 arithmetic operations \( (+, -, \times, \div ) \) with repeated use allowed.

Then we can generate a sequence of positive integers (with common difference 1) on the right side as follows (or in various other ways): \[\begin{align} 1 \times 3 - 2 &= 1 \\ 5 - 3 \times 1 &= 2 \\ 1 + 4 -2 &= 3\\ 8 \div 2 \div 1&=4\\ &\vdots, \end{align} \] where each result is obviously 1 more than the previous result.

But this can continue only up to a certain point. What is the first (least) positive integer for which this process fails to work?

Clarification: If you could generate the sequence only up to 120, your answer would be 121.

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