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A282339 A pseudorandom binary sequence with minimum variance of the absolute values of its discrete Fourier transform. 1

%I #13 Feb 28 2017 22:56:06

%S 1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,

%T 1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,1

%N A pseudorandom binary sequence with minimum variance of the absolute values of its discrete Fourier transform.

%C a(1) = 1. Each subsequent term is chosen so as to minimize the variance of the absolute values of the discrete Fourier transform of the partial sequence. If the variance doesn't change with different choices for the next term, then the complement of the previous term is used. The algorithm works on a sequence of 1's and -1's then, as a last step, all -1's are replaced by 0's.

%C This sequence is similar to A282343 where the peak-to-peak distance is considered instead of the variance.

%t varfourier[x_]:=Variance[Abs[Fourier[x]]];

%t a={1};(*First element*)

%t nmax=120;(*number of appended elements*)

%t Do[If[varfourier[Append[a,1]]<varfourier[Append[a,-1]], AppendTo[a,1], If[varfourier[Append[a,1]]>varfourier[Append[a,-1]], AppendTo[a,-1], AppendTo[a,-a[[-1]]]]],{j,nmax}];

%t a=a/.{-1->0};

%t Print[a]

%Y Cf. A280711, A280816, A282343.

%K nonn,base

%O 1,1

%A _Andres Cicuttin_, Feb 12 2017

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)