I'm not sure what is the point of eliminating 'ifs'? At any rate they can be easily replaced by e.g. 'while' loops, so in my opinion you should either eliminate both of them or none.
Again, the best way to generate such a sequence is using depth-first search or recursion. By prohibiting the usage of IFs, all solutions are inefficient (because we can't cut the tree, and are forced to follow all branches).
Back to basics 26 - Keywords
Create logical matrix with a specific row and column sums
Multiples of a Number in a Given Range
Project Euler: Problem 14 Longest Collatz sequence(harder version)
Big Integer Sqrt
Determine if input is a Narcissistic number
Put m balls into n boxes
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