%I A138967
%S A138967 1,2,3,1,4,1,2,3,1,2,3,1,4,1,2,3,1,4,1,2,3,1,2,3,1,4,1,2,3,1,2,3,1,4,1,
%T A138967 2,3,1,4,1,2,3,1,2,3,1,4,1,2,3,1,4,1,2,3,1,2,3,1,4,1,2,3,1,2,3,1,4,1,2,
%U A138967 3,1,4,1,2,3,1,2,3,1,4,1,2,3,1,2,3,1,4,1,2,3,1,4,1,2,3,1,2,3,1,4,1,2,3
%N A138967 Infinite Fibonacci word on the alphabet (1,2,3,4).
%C A138967 a(n)=3 for n=3,8,21,55,..., F(2k), k>1.
%C A138967 a(n)=4 for n=5,13,34,89,..., F(2k+1), k>1.
%C A138967 Start with the infinite Fibonacci word A003849, which is
%C A138967 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 ... and replace
%C A138967 each 0 by 1,2,3 and each 1 by 1,4; the result is A138967.
%F A138967 Let A(n)=floor(n*tau), B(n)=n+floor(n*tau); i.e., A and B are the lower 
               and upper Wythoff sequences, A=A000201, B=001950. a(n)=1 if n=A(A(k)) 
               for some k; a(n)=2 if n=B(A(k)) for some k; a(n)=3 if n=A(B(k)) for 
               some k; a(n)=4 if n=B(B(k)) for some k.
%Y A138967 Cf. A000201, A001950, A003849, A101864.
%Y A138967 Sequence in context: A097744 A055445 A135560 this_sequence A035612 A089555 
               A098554
%Y A138967 Adjacent sequences: A138964 A138965 A138966 this_sequence A138968 A138969 
               A138970
%K A138967 nonn
%O A138967 1,2
%A A138967 Clark Kimberling (ck6(AT)evansville.edu), Apr 04 2008