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A280510 Index sequence of the Thue-Morse sequence (A010060) as a block-fractal sequence. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)