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).
Calculate the height of an object dropped from the sky
Create an index-powered vector
Slicing the cube
Natural numbers in string form
Generate a vector like 1,2,2,3,3,3,4,4,4,4
Make an anonymous function that has variable output
Seperate array to small section according to its index position
Successive zeros (harder)
Determine if input is a Narcissistic number
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