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
Examples
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.
Programs
-
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 *)
Formula
a(n) = 3*A053644(n-1) for n >= 2.
Comments