|
Search: id:A108960
|
|
|
| A108960 |
|
n expressed in Fibonacci binary-like number system using only 1's and 2's. |
|
+0
1
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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 (mathar(AT)strw.leidenuniv.nl), 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
|
K. Levasseur, A Fibonacci Number System
|
|
CROSSREFS
|
Sequence in context: A163479 A017293 A120672 this_sequence A111095 A073211 A094626
Adjacent sequences: A108957 A108958 A108959 this_sequence A108961 A108962 A108963
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 22 2005
|
|
EXTENSIONS
|
More terms from David Wasserman (dwasserm(AT)earthlink.net), May 22 2008
|
|
|
Search completed in 0.002 seconds
|
