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A272532
Single bit representation of the sum of two sinusoids with periods 2 and 2*sqrt(2).
3
1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1
OFFSET
1,1
COMMENTS
Since the ratio of the two periods is irrational, the sequence is strictly non-periodic.
From the factorized expression of the corresponding real function of x : 2*cos(2Pi((2 - sqrt(2))/8)x)*sin(2Pi((2 + sqrt(2))/8)x), it is possible to see that the largest distance between consecutive zeros is not greater than the shortest semi-period, 4/(2 + sqrt(2)), that is smaller than 2, and from this it follows that there are no more than two consecutive 0's or 1's.
FORMULA
a(n) = floor( (1 + sin(2*Pi*(1/2)*n) + sin(2*Pi*(1/(2*Sqrt[2]))*n)) mod 2).
MATHEMATICA
nmax=120 ; Table[If[Sin[2*Pi*(1/2)*n]+Sin[2*Pi*(1/(2*Sqrt[2]))*n]<0, 0, 1], {n, 1, nmax}]
CROSSREFS
Conjectured quasiperiodicity in A271591 and A272170. A083035.
Sequence in context: A319843 A309847 A266786 * A166946 A144612 A174208
KEYWORD
nonn,base
AUTHOR
Andres Cicuttin, May 02 2016
STATUS
approved