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paper and pen Puzzles

Puzzles: What comes next?

Correspondent TCP July 1, 2022

0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 8, 7, 13, 8, 21, 9, 34, ?

What comes in the place of the question mark?

What comes next?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, ?