login
A273784
Frequency of the largest spectral component of the Moebius function of the first n numbers, for n>0. In case of a tie, use the smallest frequency.
2
1, 2, 2, 2, 3, 2, 4, 4, 5, 3, 6, 7, 7, 8, 8, 9, 9, 5, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 7, 18, 18, 19, 7, 20, 7, 21, 8, 8, 8, 8, 8, 24, 9, 25, 9, 26, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 32, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14
OFFSET
1,2
COMMENTS
The Discrete Fourier transform is applied to the list of Moebius function of first n numbers, then it is selected the position of the largest absolute value of the components of the transformed list. If there are several identical maxima then it is taken the lowest position of them.
A curious pattern (see link) shows that frequencies of most maximum spectral components are aligned along few convergent directions.
EXAMPLE
For the first 60 numbers starting from 1, the absolute values of the discrete Fourier transform of the Moebius function of these numbers have a maximum at position 11, then a(60) = 11.
MATHEMATICA
Table[Position[b=Abs@Fourier@Table[MoebiusMu[j], {j, 1, n}], Max[b]][[1, 1]], {n, 1, 120}]
CROSSREFS
Sequence in context: A157231 A332888 A258596 * A318058 A345901 A305434
KEYWORD
nonn
AUTHOR
Andres Cicuttin, May 30 2016
STATUS
approved