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 A282339 A pseudorandom binary sequence with minimum variance of the absolute values of its discrete Fourier transform. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. This sequence is similar to A282343 where the peak-to-peak distance is considered instead of the variance. LINKS MATHEMATICA varfourier[x_]:=Variance[Abs[Fourier[x]]]; a={1}; (*First element*) nmax=120; (*number of appended elements*) Do[If[varfourier[Append[a, 1]]varfourier[Append[a, -1]], AppendTo[a, -1], AppendTo[a, -a[[-1]]]]], {j, nmax}]; a=a/.{-1->0}; Print[a] CROSSREFS Cf. A280711, A280816, A282343. Sequence in context: A209198 A282343 A099076 * A175479 A307243 A120530 Adjacent sequences:  A282336 A282337 A282338 * A282340 A282341 A282342 KEYWORD nonn,base AUTHOR Andres Cicuttin, Feb 12 2017 STATUS approved

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Last modified May 28 00:30 EDT 2022. Contains 354110 sequences. (Running on oeis4.)