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%I #38 Aug 26 2019 08:39:23
%S 0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,
%T 1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,
%U 1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0
%N Fixed point of the morphism 0->001, 1->01.
%C This is column 1 of the array A188294.
%C Is this A003849 with another 0 in front? - _R. J. Mathar_, Apr 01 2011
%C From _Michel Dekking_, Aug 27 2016: (Start)
%C Answer: yes. Since [-x] = -[x]-1 for all non-integer x, one has for n > 1:
%C [r] - [nr] - [(1-n)r] = 1 - [nr] + [(n-1)r] + 1 = 2 - ([nr]-[(n-1)r]) = A003849(n-2). (End)
%C Also, [ns] - [(n-1)s] where s = (3-sqrt(5))/2, therefore a Sturmian sequence with slope s. Also, a fixed point under the transformation (0 ->001, 1 -> 01). - _Richard Blavy_, Nov 18 2011; transformation corrected by _Nathan Fox_, May 03 2014
%F a(n) = [r] - [n*r] - [r-n*r], where r = (1+sqrt(5))/2.
%t r = (1 + 5^(1/2))/2 + .0000000000001;
%t f[n_] := Floor[r] - Floor[n*r] - Floor[r - n*r]
%t t = Flatten[Table[f[n], {n, 1, 200}]] (* A188432 *)
%t Flatten[Position[t, 0] ] (* A026351 *)
%t Flatten[Position[t, 1] ] (* A026352 *)
%Y Cf. A188294, A096270, A026351, A026352, A003849.
%K nonn
%O 1
%A _Clark Kimberling_, Mar 31 2011
%E Name changed by _Clark Kimberling_, Aug 24 2019
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