2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, . . .

[Henry Gould]

Here is a curious sequence that might be worth adding to the OEIS:

2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, . . .

This easy sequence contains two copies of the natural number sequence 
rearranged.

It is generated by the third-order recurrence   a(n)  =  a(n-1) + a(n-2) 
-  a(n-3).

Has anyone seen this anywhere else? It is not enormously important, just 
curious.
This is one small instance that arises in my new paper
'The inverse of a finite series and a third-order recurrent sequence'
which I have just submitted to the Fibonacci Quarterly.
Henry W. Gould