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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

Table of n, a(n) for n=1..121.

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], 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 August 21 18:26 EDT 2019. Contains 326168 sequences. (Running on oeis4.)