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

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

Offset

1,2

Comments

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)

Links

Table of n, a(n) for n=1..37.

K. Levasseur, A Fibonacci Number System

Crossrefs

Sequence in context: A189330 A120672 A190642 * A111095 A073211 A233137

Adjacent sequences: A108957 A108958 A108959 * A108961 A108962 A108963

Keyword

nonn

Author

Lekraj Beedassy, Jul 22 2005

Extensions

More terms from David Wasserman, May 22 2008

Status

approved