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arithmetic n.  and  Fibonacci n.

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First numbers that belong to both sets:

1, 3, 5, 13, 21, 55, 89, 233, 377, 987, 1597, 4181, 6765, 17711, 28657, 46368, 121393, 317811, 514229, 832040, 1346269, 2178309, 5702887, 9227465.