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The sequence of numbers 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22,... (AO56964 in the OEIS), in which the nth term equals n+reversal of digits of n, poses a number of intriguing puzzles. Here just four:
Does it contain infinitely many square numbers?
Infinitely many cubes?
Infinitely many pairs...