|
Search: id:A110012
|
|
|
| A110012 |
|
a(n)=n-F(F(n)) where F(x)=floor(sqrt(2)*floor(x/sqrt(2)). |
|
+0
1
|
|
| 1, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
To built the sequence start from the infinite binary word b(k)=floor(k*(sqrt(2)-1))-floor((k-1)*(sqrt(2)-1)) for k>=1 giving 0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,...Then replace each 0 by the block {2,3,3} and each 1 by the block {2,2,3,3}. Append the initial string {1,2}.
|
|
REFERENCES
|
B. Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005
|
|
PROGRAM
|
(PARI) F(x)=floor(sqrt(2)*floor(x/sqrt(2))); a(n)=n-F(F(n))
|
|
CROSSREFS
|
Cf. A003842 (case a(n)=n-floor(phi*floor(phi^-1*n)), A006337.
Sequence in context: A049113 A055093 A081844 this_sequence A023514 A039645 A048687
Adjacent sequences: A110009 A110010 A110011 this_sequence A110013 A110014 A110015
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 02 2005
|
|
|
Search completed in 0.002 seconds
|
