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1, 2, 16, 4, 16, 16, 52, ?, 52, 16, 52, ?, 40, 52, ?

What are these question marks?

a) 8, 16, 160

b) 16, 8, 190

c) 52, 16, 160

d) 8, 25, 90

e) Impossible to determine

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Answer

a) 8, 16, 160

Reasoning

This is to do with the Collatz conjecture. The $n$th term in the sequence is the largest integer encountered when running the Collatz sequence with starting value $n$.

For example, when starting with 5, the sequence generated by the Collatz conjecture is 5,16,8,4,2,1. 16 is the highest value seen here, hence the 5th term in our sequence is 16.

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