%I #6 Feb 15 2017 03:30:31

%S 1,3,2,1,12,11,10,9,8,7,6,5,4,3,2,1,48,47,46,45,44,43,42,41,40,39,38,

%T 37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,

%U 14,13,12,11,10,9,8,7,6,5,4,3,2,1,192,191,190,189,188

%N Index sequence of the Thue-Morse sequence (A010060, using offset 1) as a reverse block-fractal sequence.

%C See A280511 for definitions. Note that the records, 3,12,48,192,... are also records in A280510, if A010060 is indexed with offset 1 instead of 0; see Example.

%e A010060 = (0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,,...) = (s(1), s(2), ... ).

%e (init. bl. #1) = (0); reversal = (0), first occurs s(1), so that a(1) = 1;

%e (init. bl. #2) = (0,1); reversal = (1,0) first occurs at s(3), so that a(2) = 3;

%e (init. bl. #3) = (0,1,1); reversal = (1,1,0) first occurs s(2), so that a(3) = 2.

%t seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}] (* A010060 *)

%t seq = StringJoin[Map[ToString, seq]]

%t breverse[seq_] := Flatten[Last[Reap[NestWhile[# + 1 &, 1, (StringLength[

%t str = StringTake[seq, Min[StringLength[seq], #]]] == # && ! (Sow[

%t StringPosition[seq, StringReverse[str], 1][[1]][[1]]]) === {}) &]]]];

%t breverse[seq] (* A280512 *) (* _Peter J. C. Moses_, Jan 01 2017 *)

%Y Cf. A010060, A280510, A280511, A280513.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Feb 10 2017