evil/odious numbers conjectures

[Ralf Stephan]

Hello, is this known/proved:

%F A001969 a(0) = 0, a(2n) = a(n) + 2n, a(2n+1) = -a(n) + 6n + 3 (conjectured).
%F A000069 a(0) = 1, a(2n) = a(n) + 2n, a(2n+1) = -a(n) + 6n + 3 (conjectured).

If true, it would make both sequences fall into the same group with
Per Noergaard's A004718 or 2^e0 (A080100).

How would one proceed the proof?

On another note, do seqfans have already seen Shallit's new book?


ralf