A280512 Index sequence of the Thue-Morse sequence (A010060, using offset 1) as a reverse block-fractal sequence.

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, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 192, 191, 190, 189, 188

Offset: 1

Author

Clark Kimberling, Feb 10 2017

Keywords

• nonn
• easy

Comments

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.

Examples

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

Crossrefs

Cf. A010060, A280510, A280511, A280513.

Programs

Mathematica

seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}]  (* A010060 *)
seq = StringJoin[Map[ToString, seq]]
breverse[seq_] := Flatten[Last[Reap[NestWhile[# + 1 &, 1, (StringLength[
str = StringTake[seq, Min[StringLength[seq], #]]] == # && ! (Sow[
StringPosition[seq, StringReverse[str], 1][[1]][[1]]]) === {}) &]]]];
breverse[seq] (* A280512 *) (* Peter J. C. Moses, Jan 01 2017 *)