Among the terms a(1) .. a(8192), 1 occurs 4095 times, 2 occurs 1024 times, 3 occurs 2048 times and 4 occurs 1025 times. No larger numbers can ever occur.

That these are the first differences of not just A091067 and A255068, but also of A060833 follows from N. Sato's Feb 12 2013 comment in the latter that "For n > 1, n is in the sequence (A060833) if and only if A038189(n-1) = 1."