In One Sequence Or Another

[Henry Gould]

Marc and Leroy - Hey! These complementary sequences are really a lot of fun!
I wrote a paper styled "Non-Fibonacci numbers", Fibonacci Quart., 3(1965),
177-183,
about the sequence complementary to 1, 2, 3, 5, 8, 13, 21, 34, . . .  and
showed
how a formula can be gotten. These non-Fibonacci numbers are in the OEIS of
course.
I was inspired by the original Beatty sequence and by the work of my old
friend
(the late) Leo Moser who was at Edmonton, Canada. The subject of
complementary
sequences was very popular among Canadian mathematicians, probably because
Samuel Beatty was in Canada in the first place. I do believe that the
complement of
a sequence (i.e. relative to the set of all natural numbers) is often well
worth studying.
We can examine the complements of thousands of sequences and the problem
then is
to say something "interesting" about them.
  ----Henry Gould