Every positive integer is either part of the sequence ⌊ *n*π ⌋ or the sequence ⌊ *n*π/(π – 1) ⌋ where *n* ranges over positive integers, and no positive integer is in both sequences.

This is a special case of Beatty’s theorem.

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Every positive integer is either part of the sequence ⌊ *n*π ⌋ or the sequence ⌊ *n*π/(π – 1) ⌋ where *n* ranges over positive integers, and no positive integer is in both sequences.

This is a special case of Beatty’s theorem.