A276870 - OEIS

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A276870

First differences of the Beatty sequence A110117 for sqrt(2) + sqrt(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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

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