I had a Cosmic Elf computer with an 1802. Wasn’t the 4004 designed as a buffer? I was thinking of the little Intel primitive 4-bit micro, a forerunner of the 8008.
I still remember when I first went to college and we were lucky to get time on a PDP1170.
What OS? Ours ran a variant of Unix PWB/6.5 called IS/1. Special Perkin-Elmer terminals with custom firmware and keycaps for efficient editing.
I was thinking of the little Intel primitive 4-bit micro, a forerunner of the 8008. I looked it up and you're correct but I seem to recall Grove saying it was originally designed as a buffer but if you look at the pin-out, it looks like a micriprocessor:
Looks like the same multiplexed bus as the 8080.
I don't remember what the PDP1170 ran.
Interestingly enough, it was at the local state university, Sac State that created the first true microcomputer (according to wiki) in 1972 based on the 8008.