Some other nice patterns in the Stern-Brocot tree:
> (brocot-string (sqrt 2) 32)
'(R L L R R L L R R L L R R L L R R L L R R L L R R L L R R L L R)
> (brocot-string (sqrt 3) 32)
'(R L R R L R R L R R L R R L R R L R R L R R L R R L R R L R R L)
> (define phi (/ (+ 1 (sqrt 5)) 2))
> (brocot-string phi 32)
'(R L R L R L R L R L R L R L R L R L R L R L R L R L R L R L R L)