[seqfan] Van Eck’s sequence (A181391).

[David Sycamore]

One of the (two) rules for this sequence is that 0 must be the next term immediately after a new term k shows up for the first time. Since a(0)=0, and this is the first time 0 appears, then by the rule the next term must be 0. But if we see this new term not just as 0 but as a(0),  then the possibility to generalise this particular rule suggests itself. 

If we modify the rule by saying that when a number k shows up for the first time, then the next number after that is a(k), (just as it is for a(0) in the original case), then this gives :

0,0,1,0,2,1,3,0,4,2,5,1... which is quite a nice sequence; the nonnegative integers interleaved with a copy of the sequence itself (in other words A025480). 

I wonder if this little fact is generally known and is of any interest? 

David.