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A276870
First differences of the Beatty sequence A110117 for sqrt(2) + sqrt(3).
3
3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3
OFFSET
1,1
LINKS
FORMULA
a(n) = floor(n*r) - floor(n*r - r), where r = sqrt(2) + sqrt(3), n >= 1.
MATHEMATICA
z = 500; r = Sqrt[2]+Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}] (* A110117 *)
Differences[b] (* A276870 *)
PROG
(PARI) vector(100, n, floor(n*(sqrt(2) + sqrt(3))) - floor((n-1)*(sqrt(2)+sqrt(3)))) \\ G. C. Greubel, Aug 16 2018
(Magma) [Floor(n*(Sqrt(2) + Sqrt(3))) - Floor((n-1)*(Sqrt(2) + Sqrt(3))): n in [1..100]]; // G. C. Greubel, Aug 16 2018
CROSSREFS
Sequence in context: A237117 A247970 A063438 * A081168 A301415 A210509
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 26 2016
STATUS
approved