|
|
A276866
|
|
First differences of the Beatty sequence A004976 for 2 + sqrt(5).
|
|
3
|
|
|
4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
(a(n+1)) is the unique fixed point of the substitution 4 -> 4445, 5 -> 44454, since alpha = sqrt(5)-2 satisfies 1/(4+alpha) = alpha. See Allouche and Shallit on characteristic words. - Michel Dekking, Jan 30 2017
|
|
REFERENCES
|
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 285.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = floor(n*r) - floor(n*r - r), where r = 2 + sqrt(5), n >= 1.
|
|
MATHEMATICA
|
z = 500; r = 2+Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A004976 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|