Polite Number - Examples and Characterization

Examples and Characterization

The first few polite numbers are

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ... (sequence A138591 in OEIS).

The impolite numbers are exactly the powers of two. It follows from the Lambek–Moser theorem that the nth polite number is ƒ(n + 1), where

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