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beatty sequences 1elementary number theory 1irrational numbers 1iterated sequences 1membership criteria 1

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math.NT2026

A Note on Iterated Beatty Sequences

Mohsen Khani, Ali N. Valizadeh, Afshin Zarei

The paper provides an elementary number‑theoretic criterion that exactly characterizes when a natural number belongs to the nth iterate of a Beatty sequence with irrational modulus…