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 A280711 A pseudorandom binary sequence with minimum cyclic autocorrelation of all of its partial subsequences. 3
 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS After the first term a(1) = 1, each subsequent term is chosen so as to minimize the cyclic autocorrelations of the partial sequence. If the autocorrelation doesn't change with different choices for the next term, then the complement of the previous term is used. If this sequence were to repeat the last term instead of using its complement, a similar result would be obtained, that is, a sequence with a nearly flat average Fourier spectrum, but with half the average power spectrum. LINKS FORMULA With F(a(n)) = Sum_{i=1..n} Sum_{j=0..n-1} (2*a(i)-1)*(2*a((i+j) mod n)-1) If argmin(F(a(n))) < argmax(F(a(n))) then    a(n) = argmin(F(a(n))) else    a(n) = (a(n-1) + 1) mod 2 MATHEMATICA (* This function is the sum of all possible cyclic autocorrelations of a list x *) AutoCorrelation[x_] :=   Sum[Abs[x.RotateRight[x, j]], {j, 0, Length[x] - 1}]; a = {1}; (* First element *) nmax = 120; (*number of appended elements*) Do[If[AutoCorrelation[Append[a, 1]] < AutoCorrelation[Append[a, -1]],    AppendTo[a, 1],    If[AutoCorrelation[Append[a, 1]] > AutoCorrelation[Append[a, -1]],     AppendTo[a, -1], AppendTo[a, -a[[-1]]]]], {j, nmax}]; a /. {-1 -> 0} CROSSREFS Sequence in context: A267635 A267034 A167364 * A293164 A230298 A000480 Adjacent sequences:  A280708 A280709 A280710 * A280712 A280713 A280714 KEYWORD nonn,base AUTHOR Andres Cicuttin, Jan 07 2017 STATUS approved

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Last modified March 23 02:37 EDT 2019. Contains 321422 sequences. (Running on oeis4.)