Here we go. Primitive recursive functions at MathWorld. That’s the reputable site I had in mind.
Okay, got that part straight. Note that the MathWorld blurb is “Fortran” oriented. Many programming languages (such as C) allow changeing the for loop parameters during the loop. That violates the condition nec. for primitive recursive.
I was thinking about a classic result by Meyer and Ritchie and their “loop” language. I can’t find out on the Net what their restriction was on loops (and my old class notes are not “easily accesible” to say the least). So for the time being, what loop restriction gives sub-primitive recursive remains a mystery to me. (I’m kinda burned out on Net searching for now. Do you know how hard it is to find “Grzegorczyk” when you don’t remember the spelling?)
And I’m now addicted to MathWorld. 