A WELL-BEHAVED COUSIN OF THE HOFSTADTER SEQUENCE

Very little is known about the Hofstadter sequence Q(n) defined by Q(1) = Q(2) = 1 and Q(n) = Q(n - Q(n - 1)) + Q(n - Q(n - 2)), n > 2. A seemingly close relative is the sequence T(n) given by T(n) = T(n - 1 - T(n - 1)) + T(n - 2 - T(n - 2)), n > 2 with T(0) = T(1) = T(2) = 1. In sharp contrast to the 'chaotic' behaviour of Q(n), T(n) behaves in a completely predictable fashion which is characterized precisely. In particular, T(n) is monotonic and hits every positive integer.