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).
The Goldbach Conjecture, Part 2
Get the area codes from a list of phone numbers
Sum of diagonal of a square matrix
Getting the indices from a vector
Celsius to Kelvin
Determine if input is a Narcissistic number
Successive zeros (harder)
Find the right number make the equation
Generate a vector like 1,2,2,3,3,3,4,4,4,4
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