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).
Find the palindrome
Check if sorted
All your base are belong to us
Free passes for everyone!
Find the right number make the equation
Put m balls into n boxes
Generate a vector like 1,2,2,3,3,3,4,4,4,4
Successive zeros (harder)
Return fibonacci sequence do not use loop and condition
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