The infinite sequence is defined as follows:
a₁=1
for n ≥ 1, a_2n= a_n+1
a_2n+1=1/ a_2n

Prove that every positive rational number occurs in the sequence exactly once.

The numerators of this sequence are OEIS A020650, and the denominators are OEIS A020651.

Posted by Brian Smith on 2016-08-27 10:46:54