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

1,2

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.

Links

Table of n, a(n) for n=1..69.

Example

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.

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 *)

Crossrefs

Cf. A010060, A280510, A280511, A280513.

Sequence in context: A059418 A092582 A213262 * A068440 A246381 A048647

Adjacent sequences: A280509 A280510 A280511 * A280513 A280514 A280515

Keyword

nonn,easy

Author

Clark Kimberling, Feb 10 2017

Status

approved