#!/usr/bin/python def digits(n): while n > 0: yield n % 10 n //= 10 def reduce(n): product = 1 for d in digits(n): product *= d return product memo = {} def persistence(n, steps): steps += 1 if n in memo: n = memo[n] else: n = reduce(n) if n < 10: return steps else: return persistence(n, steps) threshold = 1 for i in range(10, 1000000): if persistence(i, 0) >= threshold: print(threshold, i) threshold += 1 # TODO: Only search integers with digits in sorted order.
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