A282343 A pseudorandom binary sequence with minimum peak to peak distance of the absolute values of its discrete Fourier transform.

1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1

Offset

1,1

Comments

a(1) = 1. Each subsequent term is chosen so as to minimize the peak to peak distance of the absolute values of the discrete Fourier transform of the partial sequence. If the peak to peak distance 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 A282339 where it is considered the variance instead of the peak to peak distance.

Links

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

Mathematica

peaktopeakfourier[x_] := Max[Abs[Fourier[x]]] - Min[Abs[Fourier[x]]];
a = {1}; (*First element*)
nmax = 120; (*number of appended elements*)
Do[If[peaktopeakfourier[Append[a, 1]] <
   peaktopeakfourier[Append[a, -1]], AppendTo[a, 1],
  If[peaktopeakfourier[Append[a, 1]] >
    peaktopeakfourier[Append[a, -1]], AppendTo[a, -1],
   AppendTo[a, -a[[-1]]]]], {j, nmax}];
a = a /. {-1 -> 0};
print[a]

Crossrefs

Cf. A280711, A280816, A282339.

Sequence in context: A000480 A118251 A209198 * A099076 A282339 A175479

Adjacent sequences: A282340 A282341 A282342 * A282344 A282345 A282346

Keyword

nonn,base

Author

Andres Cicuttin, Feb 12 2017

Status

approved