On primitive recursive permutations and their inverses
Frank B. Cannonito, Mark S. Finkelstein · Journal of Symbolic Logic · 1970
It has been known for some time that there is a primitive recursive permutation of the nonnegative integers whose inverse is recursive but not primitive recursive. For example one has this result apparently for the first time in Kuznecov [1] and implicitly in Kent [2] or J. Robinson [3], who shows that every singularly recursive function ƒ is representable as where A, B, C are primitive recursive and B is a permutation.