login
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
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 *)
Differences[b] (* A276866 *)
CROSSREFS
Sequence in context: A228729 A174444 A268237 * A331842 A006264 A134994
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 24 2016
STATUS
approved