We present a novel approach to a remarkable function
D: N_0→N_0 defined by D(0)=0, D(1)=1, D(2n)=D(n), D(2n+1)=D(n)+D(n+1), studied independently by well known researchers in different areas of mathematics and computer science. Besides some
known properties we add some new ones (including a relation to the
(Eisenstein-)Stern\u27s diatomic sequence). Some historical remarks are added at the end of this paper
