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 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 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

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Last modified June 30 19:12 EDT 2022. Contains 354945 sequences. (Running on oeis4.)