In One Sequence Or Another (counter-intuitive?)

[Marc LeBrun]

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.