cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A280510 #5 Feb 15 2017 03:30:23
%S A280510 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 A280510 48,48,48,48,48,48,48,48,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,
%U A280510 96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,192
%N A280510 Index sequence of the Thue-Morse sequence (A010060) as a block-fractal sequence.
%C A280510 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 A280510 a(n) = 3*A053644(n-1) for n >= 2.
%e A280510 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 A280510 (initial block #1) = (0) first repeats at s(3), so that a(1) = 3;
%e A280510 (initial block #2) = (0,1) first repeats at s(3), so that a(2) = 3;
%e A280510 (initial block #3) = (0,1,1) first repeats at s(6), so that a(3) = 6.
%t A280510 seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}]  (* A010060 *)
%t A280510 seq = StringJoin[Map[ToString, seq]]
%t A280510 u = -1 + Most[Flatten[Rest[Reap[NestWhile[# + 1 &, 1,
%t A280510 Sow[First[Last[StringPosition[seq, StringTake[seq, #], 2]]]] >
%t A280510 1 &]]]]] (* A280510 *)  (* _Peter J. C. Moses_, Jan 05 2017 *)
%Y A280510 Cf. A010060, A280511, A280512.
%K A280510 nonn,easy
%O A280510 1,1
%A A280510 _Clark Kimberling_, Feb 10 2017