A280510 - OEIS

%I #5 Feb 15 2017 03:30:23

%S 3,3,6,6,12,12,12,12,24,24,24,24,24,24,24,24,48,48,48,48,48,48,48,48,

%T 48,48,48,48,48,48,48,48,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,

%U 96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,192

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

%C 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)).

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

%e 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), ... ).

%e (initial block #1) = (0) first repeats at s(3), so that a(1) = 3;

%e (initial block #2) = (0,1) first repeats at s(3), so that a(2) = 3;

%e (initial block #3) = (0,1,1) first repeats at s(6), so that a(3) = 6.

%t seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}]  (* A010060 *)

%t seq = StringJoin[Map[ToString, seq]]

%t u = -1 + Most[Flatten[Rest[Reap[NestWhile[# + 1 &, 1,

%t Sow[First[Last[StringPosition[seq, StringTake[seq, #], 2]]]] >

%t 1 &]]]]] (* A280510 *)  (* _Peter J. C. Moses_, Jan 05 2017 *)

%Y Cf. A010060, A280511, A280512.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Feb 10 2017