2+3=5

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Find the next number in the following sequence

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


The answer is 58.

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1 solution

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

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