Output the nth rational number according to the Stern-Brocot sequence
Haskell, 78 77 65 58 bytes

Shamelessly stealing the optimized approach gives us:

(s#t)0=show s++'/':show t
(s#t)n=t#(s+t-2*mod s t)$n-1
1#1


Thanks to @nimi for golfing a few bytes using an infix function!

(Still) uses 0-based indexing.



The old approach:

s=(!!)(1:1:f 0)
f n=s n+s(n+1):s(n+1):(f$n+1)
r n=show(s n)++'/':(show.s$n+1)


Damn the output format... And indexing operators. EDIT: And precedence.

Fun fact: if heterogenous lists were a thing, the last line could be:

r n=show&gt;&gt;=[s!!n,'/',s!!(n+1)]