|
Search: id:A014675
|
|
|
| A014675 |
|
The infinite Fibonacci word (start with 1, apply 1->2, 2->21, take limit). |
|
+0
14
|
|
| 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
REFERENCES
|
M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151.
J. Grytczuk, Infinite semi-similar words, Discrete Math. 161 (1996), 133-141.
G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol. 4, no. 1, 1997, pp. 34-42, esp. p. 36.
G. Melancon, Lyndon factorization of sturmian words, Discr. Math., 210 (2000), 137-149.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..10945 (20 iterations)
|
|
FORMULA
|
Define strings S(0)=1, S(1)=2, S(n)=S(n-1)S(n-2); iterate. Sequence is S(infinity).
a(n) = [(n+1)*phi] - [n*phi], phi =(1+ sqrt 5)/2.
|
|
MAPLE
|
Digits := 50: t := evalf( (1+sqrt(5))/2); A014675 := n->floor((n+1)*t)-floor(n*t);
|
|
MATHEMATICA
|
Nest[ Flatten[ # /. {1 -> 2, 2 -> {2, 1}}] &, {1}, 11] (* Robert G. Wilson v *)
|
|
CROSSREFS
|
This is the 1, 2 version. The standard form is A003849. See also A005614. First differences of A000201.
Cf. A082389.
Differs from A025143 in many entries starting at entry 8. Same as A001468 if an initial 1 is added.
Cf. A008351.
Sequence in context: A080634 A109925 A001468 this_sequence A107362 A166332 A022303
Adjacent sequences: A014672 A014673 A014674 this_sequence A014676 A014677 A014678
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Corrected by N. J. A. Sloane (njas(AT)research.att.com), Nov 07, 2001
|
|
|
Search completed in 0.002 seconds
|
