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).
Project Euler: Problem 1, Multiples of 3 and 5
Project Euler: Problem 3, Largest prime factor
Stuff the Board
Dimensions of a rectangle
Sum of odd numbers in a matrix
Find the right number make the equation
Find the maximum two numbers of every column of a matrix
Compute the intersect point of line and plan
Big Integer Sqrt
Generate a vector like 1,2,2,3,3,3,4,4,4,4
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