A280510 Index sequence of the Thue-Morse sequence (A010060) as a block-fractal sequence.

3, 3, 6, 6, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 24, 24, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 192

Offset

1,1

Comments

The index sequence (a(n)) of a block-fractal sequence (s(n)) is defined by a(n) = least k > 0 such that (s(k), s(k+1), ..., s(k+n)) = (s(0), s(1), ..., s(n)).

Links

Table of n, a(n) for n=1..65.

Formula

a(n) = 3*A053644(n-1) for n >= 2.

Example

A010060 = (0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,,...) = (s(0), s(1), ... ).
(initial block #1) = (0) first repeats at s(3), so that a(1) = 3;
(initial block #2) = (0,1) first repeats at s(3), so that a(2) = 3;
(initial block #3) = (0,1,1) first repeats at s(6), so that a(3) = 6.

Mathematica

seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}]  (* A010060 *)
seq = StringJoin[Map[ToString, seq]]
u = -1 + Most[Flatten[Rest[Reap[NestWhile[# + 1 &, 1,
Sow[First[Last[StringPosition[seq, StringTake[seq, #], 2]]]] >
1 &]]]]] (* A280510 *)  (* Peter J. C. Moses, Jan 05 2017 *)

Crossrefs

Cf. A010060, A280511, A280512.

Sequence in context: A131942 A240204 A200905 * A292128 A117775 A243307

Adjacent sequences: A280507 A280508 A280509 * A280511 A280512 A280513

Keyword

nonn,easy

Author

Clark Kimberling, Feb 10 2017

Status

approved