Level
pending

Find the next number in the following sequence

$01,12,35,81,32,13,45,......$

The answer is 58.

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This is a sequence of pairs of digits of the sequence of Fibonacci numbers.

$F = \{0,1,1,2,3,5,8,13,21,34,55,89,...\} \\ \Rightarrow S = \{01,12,35,81,32,13,45,\boxed{58},...\}$