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 sum of all the numbers of the input vector
Project Euler: Problem 16, Sums of Digits of Powers of Two
Return unique values without sorting
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Successive zeros (harder)
Solve Sudoku puzzle step by
Find the maximum two numbers of every column of a matrix
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