A276866 - OEIS

A276866

First differences of the Beatty sequence A004976 for 2 + sqrt(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, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4

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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

Clark Kimberling, Table of n, a(n) for n = 1..10000

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

Cf. A004976, A276884.

Sequence in context: A228729 A174444 A268237 * A331842 A006264 A134994

Adjacent sequences: A276863 A276864 A276865 * A276867 A276868 A276869

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 24 2016

STATUS

approved