%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 binarylike 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 nonunique 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
