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 A276864 First differences of the Beatty sequence A001952 for 2 + sqrt(2). 5
 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Shifted by 1 (as one should) this is the unique fixed point of the morphism 3 -> 34, 4 -> 343. See A159684. - Michel Dekking, Aug 25 2019 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 FORMULA a(n) = floor(n*r) - floor(n*r - r), where r = 2 + sqrt(2), n >= 1. a(n) = 2 + floor(n*sqrt(2)) - floor((n-1)*sqrt(2)). - Andrew Howroyd, Feb 15 2018 MATHEMATICA z = 500; r = 2+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A001952 *) Differences[b] (* A276864 *) PROG (PARI) a(n) = 2 + sqrtint(2*n^2) - sqrtint(2*(n-1)^2) \\ Andrew Howroyd, Feb 15 2018 (Magma) [Floor(n*(2 + Sqrt(2))) - Floor((n-1)*(2 + Sqrt(2))): n in [1..100]]; // G. C. Greubel, Aug 16 2018 CROSSREFS Cf. A001952, A006337, A276882. Sequence in context: A091282 A202708 A027684 * A342928 A236442 A046537 Adjacent sequences: A276861 A276862 A276863 * A276865 A276866 A276867 KEYWORD nonn,easy AUTHOR Clark Kimberling, Sep 24 2016 EXTENSIONS Name corrected by Michel Dekking, Aug 25 2019 STATUS approved

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Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)