Regarding 2 related sequences
- From: "Leroy Quet" <qqquet@xxxxxxxxxxxxxx>
- Date: 30 Mar 2006 10:44:52 -0800
Regarding 2 related sequences in the Encyclopedia of Integer Sequences:
( http://www.research.att.com/~njas/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
.
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