The Katydid sequence is a sequence of numbers first defined in Clifford A. Pickover's book Wonders of Numbers (2001).
[1] For instance, applying the first operation to 1 produces the number 4, and applying the second operation to 4 produces the number 35, both of which are in the sequence.
The first 10 elements of the sequence are:[2] Pickover asked whether there exist numbers that can be reached by more than one sequence of operations.
For instance, 1814526 can be reached by the two sequences 1, 4, 10, 22, 46, 329, 660, 4627, 9256, 18514, 37030, 259217, 1814526 and 1, 14, 30, 62, 441, 884, 1770, 3542, 7086, 14174, 28350, 56702, 113406, 226814, 453630, 907262, 1814526.
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