

A280510


Index sequence of the ThueMorse sequence (A010060) as a blockfractal 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
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OFFSET

1,1


COMMENTS

The index sequence (a(n)) of a blockfractal 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(n1) 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



