The HAP-subsequence structure of that sequence

The sequence that can be seen displayed here has the following subsequence structure. We refer to the sequence [math]\displaystyle{ x_d,x_{2d},\dots }[/math] as the d-sequence, and we write (a,b;c,d,e) to mean that the a- and b-sequences are almost identical and almost equal to minus the c-, d- and e-sequences.

(1,32;7) (2,21;3,14) (4,9;5,6,28) (8,11,15,18;10,12,17,19,27) (13,20,24;16,22,25,30)

The 23-, 26-, 29- and 31-sequences appear to be "sporadic". The 26-sequence ought, by multiplicativity, to be minus the 1-sequence, but although it starts that way it fairly soon degenerates. We still have no clear understanding of why these deviations from multiplicativity take place or whether there is any system to them.