The prime then composite recurrence; a(2n) = a(2n-1)-th prime and a(2n+1) = a(2n)-th composite and a(1) = 1.

A064960

The prime then composite recurrence; a(2n) = a(2n-1)-th prime and a(2n+1) = a(2n)-th composite and a(1) = 1.