There is a surprising connection with the Thue-Morse sequence A010060. If the k-th run of equal terms in A010060 (k>=0) has length L (L=1 or 2, see A026465), replace it with 2L copies of the pair 4k+1, 4k+3. This produces the current sequence apart from the initial 1: 0 1 1 0 1 0 0 1 ... becomes 1 3 1 3 5 7 5 7 5 7 5 7 9 11 9 11 13 ... - N. J. A. Sloane, Dec 31 2013