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A081147 First differences of A022839.

%I A081147 #21 Jan 16 2024 06:56:31
%S A081147 2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,
%T A081147 2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,
%U A081147 2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2
%N A081147 First differences of A022839.
%C A081147 Differences of Beatty sequence for square root of 5.
%C A081147 Let S(0) = 2; obtain S(k) from S(k-1) by applying 2 -> 2223, 3 -> 22223; sequence is S(0), S(1), S(2), ...
%H A081147 G. C. Greubel, <a href="/A081147/b081147.txt">Table of n, a(n) for n = 0..10000</a>
%F A081147 a(n) = floor((n+1)*sqrt(5)) - floor(n*sqrt(5)).
%t A081147 Flatten[ Table[ Nest[ Flatten[ # /. {2 -> {2, 2, 2, 3}, 3 -> {2, 2, 2, 2, 3}}] &, {2}, n], {n,0,4}]] (* _Robert G. Wilson v_, May 07 2005 *)
%t A081147 Differences[Table[Floor[n Sqrt[5]],{n,0,110}]] (* _Harvey P. Dale_, May 05 2019 *)
%o A081147 (PARI) a(n)=floor((n+1)*sqrt(5))-floor(n*sqrt(5))
%o A081147 (Magma)
%o A081147 A081147:= func< n | Floor((n+1)*Sqrt(5)) - Floor(n*Sqrt(5)) >;
%o A081147 [A081147(n): n in [0..120]]; // _G. C. Greubel_, Jan 15 2024
%o A081147 (SageMath)
%o A081147 def A081147(n): return floor((n+1)*sqrt(5)) - floor(n*sqrt(5))
%o A081147 [A081147(n) for n in range(121)] # _G. C. Greubel_, Jan 15 2024
%Y A081147 Cf. A022839, A081168.
%K A081147 nonn
%O A081147 0,1
%A A081147 _Benoit Cloitre_, Apr 16 2003