%I #26 Jan 17 2024 01:52:40

%S 3,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,

%T 3,3,4,3,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,

%U 3,3,3,3,3,4,3,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4,3,3,3,3,3,4

%N Differences of Beatty sequence for square root of 10.

%C Let S(0) = 3; obtain S(k) from S(k-1) by applying the morphism 3 -> 333334, 4 -> 3333334; sequence is S(0), S(1), S(2), ...

%C More generally, for a(n,m) = floor((n+1)*sqrt(m^2+ 1)) - floor(n*sqrt(m^2+1)) start with m and apply the morphism: m -> m^(2m-1), m+1; m+1 -> m^(2m), m+1.

%H G. C. Greubel, <a href="/A081168/b081168.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = floor((n+1)*sqrt(10)) - floor(n*sqrt(10)).

%t Differences[Floor[Sqrt[10]*Range[0, 120]]] (* _G. C. Greubel_, Jan 15 2024 *)

%o (PARI) a(n)=floor((n+1)*sqrt(10))-floor(n*sqrt(10))

%o (Magma)

%o A081168:= func< n | Floor((n+1)*Sqrt(10)) - Floor(n*Sqrt(10)) >;

%o [A081168(n): n in [0..120]]; // _G. C. Greubel_, Jan 15 2024

%o (SageMath)

%o def A081168(n): return floor((n+1)*sqrt(10)) - floor(n*sqrt(10))

%o [A081168(n) for n in range(121)] # _G. C. Greubel_, Jan 15 2024

%Y Cf. A010467, A006337, A177102.

%K nonn

%O 0,1

%A _Benoit Cloitre_, Apr 16 2003