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Problem of the Week 1181

A Singular Function

Let a(n) be the total number of digits that are 1 that occur in 1, 2, 3, ..., n. Example: a(100) = 21. True or False: a(n) < n for all n >= 2.

Source: Suggested by Ed Barbeau, who cites an article by Peter Vanden Bosch: A singular function: A problem-solving parable, The Mathematics Teacher, 90 (1997), 390-393.

© Copyright 2014 Stan Wagon. Reproduced with permission.

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8 June 2014