Does there exist a sequence
of non-negative integers that simultaneously satisfies the following three conditions?
(a) Each of the integers
occurs in the sequence.
(b) Each positive integer occurs in the sequence infinitely often.
(c) For any
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Does there exist a sequence $F(1), F(2), F(3), \ldots$ of non-negative integers that simultaneously satisfies the following three conditions?
(a) Each of the integers $0, 1, 2, \ldots$ occurs in the sequence.
(b) Each positive integer occurs in the sequence infinitely often.
(c) For any $n \geq 2,$
$$F(F(n^{163})) = F(F(n)) + F(F(361)).$$
Školjka