In One Sequence Or Another (counter-intuitive?)
Marc LeBrun
mlb at fxpt.com
Thu Mar 25 20:04:56 CET 2004
Leroy, thanks for an interesting observation.
Another way to put it might be something like:
Every monotonic function f with its inverse g partitions all suitably large
integers into two disjoint increasing sequences, namely floor(f(n))+n and
ceiling(g(n))+n-1.
So I guess if we submit a sequence with a nice formula we might want to see
if we can invert it, and submit the complement too.
This also suggests possible extensions for superseeker: given any
increasing sequence you might want to look for its complement. And given
any positive sequence you could look for the complement of its sum. And so on.
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