Math Questions: A096216 & A116537

[Leroy Quet]

Regarding 2 related sequences:

Sequence A096216 is (paraphrasing the official name of the sequence):
a(1)=1, a(n) = the number of earlier terms of the sequence which are 
coprime to n.

While sequence A116537 is (again paraphrasing):
a(1)=1, a(n) = the number positive integers which are coprime to n, are 
<= n, and do _not_ occur among the earlier terms of the sequence.


First, is A096216 such that a(2n) is always <= to both a(2n+1) and 
a(2n-1)?

(Calculating a few more terms of the sequence A116537, however, shows an 
exception to the strict zig-zaggedness of that sequence.) 

Also, it SEEMS like the limits, where {a(k)} is either sequence,

(1/n^2) * sum{k=1 to n} a(k), as n -> inf,

approaches one of two nonzero finite constants, the constant depending on 
which sequence is {a(k)}.
(I base my conjecture that the two limits are nonzero finite constants 
based solely upon the behavior of the limits for n = 20. Could someone 
test this for, say, n = 1000 or higher?)

thanks,
Leroy Quet