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A108960
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n expressed in Fibonacci binary-like number system using only 1's and 2's.
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0
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1, 2, 12, 22, 121, 221, 122, 1211, 2211, 1221, 1212, 2212, 1222, 2222, 12211, 12121, 22121, 12221, 22221, 12212, 12122, 22122, 12222, 121211, 221211, 122211, 222211, 122121, 121221, 221221, 122221, 121212, 221212, 122212, 222212, 122122, 121222
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OFFSET
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1,2
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COMMENTS
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We have, for instance, a(16)=12121 because 16 = 1*(5) + 2*(3) + 1*(2) + 2*(1) + 1*(1) = 1*F(5) + 2*F(4) + 1*F(3) + 2*F(2) + 1*F(1).
Comments from R. J. Mathar, Feb 12 2008 (Start) (i) The representation chosen here is that the leftmost digit of a(n) refers to the coefficient of F(1)=1, the second from the left to the coefficient of F(2)=1 etc.
(ii) If one would minimize the length of the representation, one would select a(8)=222 = 2*F(1)+2*F(2)+2*F(3)=2*1+2*1+2*2, with 3 digits, not a(8)=1211 =1*F(1)+2*F(2)+1*F(3)+1*F(4) with four digits.
(iii) If one would minimize the decimal value of a(n), one would get the sequence 1, 2, 12, 22, 121, 112, 122, 222, 1121, 1112 etc.
We are essentially dealing with the output of a web program which does not document which of the non-unique representations is actually chosen. (End)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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