%I #13 Jan 16 2024 13:21:55

%S 1,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,

%T 1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,

%U 1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,1,2

%N Differences of Beatty sequence for cube root of 3.

%H Harvey P. Dale, <a href="/A081129/b081129.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor((n+1)*3^(1/3)) - floor(n*3^(1/3)).

%t Differences[Floor[Range[0,110]Surd[3,3]]] (* _Harvey P. Dale_, Apr 06 2022 *)

%o (PARI) a(n)=floor((n+1)*3^(1/3))-floor(n*3^(1/3))

%o (Magma)

%o A081129:= func< n | Floor((n+1)*3^(1/3)) - Floor(n*3^(1/3)) >;

%o [A081129(n): n in [0..120]]; // _G. C. Greubel_, Jan 15 2024

%o (SageMath)

%o def A081129(n): return floor((n+1)*3^(1/3)) - floor(n*3^(1/3))

%o [A081129(n) for n in range(121)] # _G. C. Greubel_, Jan 15 2024

%Y Cf. A059539, A081117, A081147, A081168.

%K nonn

%O 0,3

%A _Benoit Cloitre_, Apr 16 2003