The following iterative sequence is defined for the set of positive integers:
- n → n/2 (n is even)
- n → 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
- Write a method
even_next(n)
that returns the next value in the sequence for an even inputn
- Write a method
odd_next(n)
that returns the next value in the sequence for an odd inputn
- Write a method
next_value(n)
that returns the next value in the sequence for any (integer) inputn
- Write a method
collatz(n)
that returns the Collatz sequence from n to 1, in an array - Write a method
longest_collatz
that returns the starting number under one million that returns the longest sequence - Run
learn
until you get all of the RSpec tests to pass.
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