cp's OEIS Frontend

A122497 Let f(S) denote the interchange of 1's and 2's in S. Let S_0 = 1, S_{N+1} = f(S_N).S_N, where the dot indicates concatenation. Sequence gives S_0.S_1.S_2.S_3....

%I A122497 #26 Feb 16 2025 08:33:02
%S A122497 1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,
%T A122497 2,1,2,2,1,1,2,2,1,2,1,1,2,1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,1,2,2,1,2,
%U A122497 1,1,2,2,1,1,2,1,2,2,1,2,1,1,2,1,2,2,1,1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,1,2
%N A122497 Let f(S) denote the interchange of 1's and 2's in S. Let S_0 = 1, S_{N+1} = f(S_N).S_N, where the dot indicates concatenation. Sequence gives S_0.S_1.S_2.S_3....
%C A122497 An alternating triangular Morse-Thue sequence based on A010060 using {1,2} instead of {0,1} substitutions.
%H A122497 G. C. Greubel, <a href="/A122497/b122497.txt">Table of n, a(n) for the first 13 rows, flattened</a>
%H A122497 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Thue-MorseConstant.html">Thue-Morse Constant</a>
%F A122497 a(n) = A059448(n) + 1. - _Filip Zaludek_, Dec 10 2016
%e A122497 The first few S_i are:
%e A122497 1
%e A122497 2, 1
%e A122497 1, 2, 2, 1
%e A122497 2, 1, 1, 2, 1, 2, 2, 1
%e A122497 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1
%t A122497 ThueMorse[n_, b_] := Nest[Flatten[ # /. {1 -> {1, 2}, 2 -> {2, 1}}] &, {b}, n] a = Table[ThueMorse[n, 1 + Mod[n, 2]], {n, 0, 7}] Flatten[a]
%Y A122497 Cf. A010060, A014571, A014572, A074072, A074073.
%K A122497 nonn,tabf
%O A122497 1,2
%A A122497 _Roger L. Bagula_, Sep 15 2006
%E A122497 Edited by _N. J. A. Sloane_, May 22 2007