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Pickover asked whether there exist numbers that can be reached by more than one sequence of operations. The answer is yes. For instance, 1814526 can be reached by the two sequences
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A Katydid sequence is the smallest sequence of integers that can be reached from 1 by a sequence of the two operations
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1, 14, 30, 62, 441, 884, 1770, 3542, 7086, 14174, 28350, 56702, 113406, 226814, 453630, 907262, 1814526
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1, 4, 10, 22, 46, 329, 660, 4627, 9256, 18514, 37030, 259217, 1814526
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