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A108960 n expressed in Fibonacci binary-like number system using only 1's and 2's. 0

%I

%S 1,2,12,22,121,221,122,1211,2211,1221,1212,2212,1222,2222,12211,12121,

%T 22121,12221,22221,12212,12122,22122,12222,121211,221211,122211,

%U 222211,122121,121221,221221,122221,121212,221212,122212,222212,122122,121222

%N n expressed in Fibonacci binary-like number system using only 1's and 2's.

%C 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).

%C 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.

%C (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.

%C (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.

%C 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)

%H K. Levasseur, <a href="http://www.hostsrv.com/webmaa/app1/MSP/webm1010/fibonaccinumbersystem">A Fibonacci Number System</a>

%K nonn

%O 1,2

%A _Lekraj Beedassy_, Jul 22 2005

%E More terms from _David Wasserman_, May 22 2008

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Last modified January 29 17:05 EST 2023. Contains 359923 sequences. (Running on oeis4.)