It was a radio hit some three decades back. I remember hearing it a lot, but never found out who did it. The lead instrument on the theme was an alto sax.
When I reconstructed it from memory on guitar, I played it in E, because guitar. More likely, it was really in either F or E-flat, because sax. I’ll give it in F, best I can:
A - C - F;
F - A - D;
C… Bb A, G, F (repeat)
After that comes a variant where the third note F and the sixth note D are played at the octave.
One distinctive thing about this tune is the type of syncopation. Every note (except that B-flat) is played an eighth-note off the beat. It comes in an eighth-note before the downbeat. How many tunes ever do that? IIRC it had a touch of swing underlying the heavy syncopation, making it more rhythmically sophisticated than it seems at first. It used a fairly bright tempo too.
I listened to every pop jazz hit I could think of from the 1970s and '80s but never found it.
Excellent Straight Dope coup, Chingon! Thank you!