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%I #26 Apr 07 2020 22:01:09
%S 0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,
%T 1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,
%U 0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,1,0,0
%N Trajectory of 0 under the morphism 0 -> 0001101, 1 -> 0011001.
%C In some bar codes, the 0's and 1's on the left represent digits according to the following code:
%C 0 = 0001101,
%C 1 = 0011001,
%C 2 = 0010011,
%C ...,
%C 9 = 0001011.
%C This sequence could then be loosely described as its own bar code.
%C (This assumes the sequence has no "guard digits" at the start, is infinite, and only uses the "left half" coding.)
%H David A. Corneth, <a href="/A274950/b274950.txt">Table of n, a(n) for n = 0..10002</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e Start with 0 -> 0001101, so we have 0001101. The second digit is 0, so we concatenate 0001101 which gives 00011010001101. The third digit is 0, so we concatenate 0001101 again which gives 000110100011010001101. The fourth digit is 1 so we concatenate 0011001 to get 0001101000110100011010011001, etc. - _David A. Corneth_, Aug 03 2017
%t Nest[Flatten[# /. {0 -> {0, 0, 0, 1, 1, 0, 1}, 1 -> {0, 0, 1, 1, 0, 0, 1}}] &, 0, 3] (* _Michael De Vlieger_, Aug 03 2017 *)
%o (PARI) first(n) = {my(res = [0, 0, 0, 1, 1, 0, 1], i = 2, m = Map(Mat([0,[0, 0, 0, 1, 1, 0, 1];1,[0, 0, 1, 1, 0, 0, 1]]))); while(#res < n, res = concat(res, mapget(m, res[i])); i++); res} \\ _David A. Corneth_, Aug 03 2017
%Y Cf. A191818.
%K nonn
%O 0
%A _N. J. A. Sloane_, Aug 04 2016
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