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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
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 24 2016
EXTENSIONS
Name corrected by Michel Dekking, Aug 25 2019
STATUS
approved