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A152306 Simple 'chaotic' sequence: a(n)=floor(log(2)*((1 + sqrt(3))/2)^n) mod 10. 0

%I

%S 0,0,1,1,2,3,4,6,8,1,5,1,9,9,4,4,1,9,0,9,4,4,2,4,5,7,5,9,2,6,7,5,9,2,

%T 2,4,0,2,2,8,5,4,7,9,8,3,8,4,9,1,6,1,4,5,3,0,7,2,6,3,6,8,1,5,1,3,9,6,

%U 0,9,9,8,3,8,5,9,1,1,7,7,1,5,5,8,6,5,3,6,8,1,0,0,6,6,9,8,2,2,8,9,8

%N Simple 'chaotic' sequence: a(n)=floor(log(2)*((1 + sqrt(3))/2)^n) mod 10.

%C Derived from the Mathematica generated binet:

%C f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == a[n - 2] + a[n - 3] + a[n - 1]/10,a[0] == 1, a[1] == 1, a[2] == 1}, a[n], n][[1]] // FullSimplify] ;

%C by plotting the 3 parts in 3D and recognizing that the real part was the major

%C contributor to the sequence and using the nearest constants in that part.

%F a(n)=floor(log(2)*((1 + sqrt(3))/2)^n) mod 10

%t Clear[f]; f[n_] = Log[2]*((1 + Sqrt[3])/2)^n;

%t Table[Mod[Floor[f[n]], 10], {n, 0, 100}]

%K nonn,less

%O 0,5

%A _Roger L. Bagula_, Dec 02 2008

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Last modified January 17 19:43 EST 2022. Contains 350403 sequences. (Running on oeis4.)