[bluesbassman]

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As Philo stated, there is no reason to favor the number 61 over F(18) as the next number in the sequence.

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there is plenty of reason. when "61" is the answer, you can explain the result in like 5 words. Id bet some children could get 61.

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Of course I meant there is no mathematical reason to choose one solution over another. You claimed 61 "must" be the next number in the sequence, and challenged someone to construct an alternative rule (i.e. function) that gives a different solution, which is exactly what I did. (And my solution can be understood with grade school level math.)

Obviously, given how our pattern-seeking brains understand mathematics, the sequence of primes is the most intuitive or natural solution. But that solution is not unique, which was Philo's original (and correct) point.