

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 peaktopeak 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



