OFFSET
1,4
LINKS
Christopher Hunt Gribble, Flattened irregular triangle, for j = 2..100 and k = 1..j-1.
EXAMPLE
The values are listed horizontally in increasing order for each (j, k) under the column headed "cos(2*Pi/k) mod j".
The column headed "nov" is the number of values. The values read downwards form A164822.
I call "cos(x) mod j" the "Discrete Cosine of x modulo j".
cos(2*Pi/k) mod j can be calculated by expressing cos(2*Pi) as a polynomial P in cos(2*Pi/k), for which the coefficients are those of Chebyshev's T(n,x) polynomials (A053120), and then solving P - 1 == 0 (mod j) by trial and error.
...j.......k.....nov....cos(2*Pi/k).mod.j
...2.......1.......1.......1
...3.......1.......1.......1
...........2.......2.......1.......2
...4.......1.......1.......1
...........2.......2.......1.......3
...........3.......1.......1
...5.......1.......1.......1
...........2.......2.......1.......4
...........3.......2.......1.......2
...........4.......2.......1.......4
...6.......1.......1.......1
...........2.......4.......1.......2.......4.......5
...........3.......1.......1
...........4.......5.......1.......2.......3.......4.......5
...........5.......1.......1
...7.......1.......1.......1
...........2.......2.......1.......6
...........3.......2.......1.......3
...........4.......2.......1.......6
...........5.......1.......1
...........6.......4.......1.......3.......4.......6
...8.......1.......1.......1
...........2.......4.......1.......3.......5.......7
...........3.......1.......1
...........4.......7.......1.......2.......3.......4.......5.......6.......7
...........5.......1.......1
...........6.......4.......1.......3.......5.......7
...........7.......1.......1
...9.......1.......1.......1
...........2.......2.......1.......8
...........3.......3.......1.......4.......7
...........4.......4.......1.......3.......6.......8
...........5.......1.......1
...........6.......6.......1.......2.......4.......5.......7.......8
...........7.......1.......1
...........8.......4.......1.......3.......6.......8
..10.......1.......1.......1
...........2.......4.......1.......4.......6.......9
...........3.......2.......1.......7
...........4.......5.......1.......4.......5.......6.......9
...........5.......1.......1
...........6.......8.......1.......2.......3.......4.......6.......7.......8.......9
...........7.......1.......1
...........8.......5.......1.......4.......5.......6.......9
...........9.......2.......1.......7
..11.......1.......1.......1
...........2.......2.......1......10
...........3.......2.......1.......5
...........4.......2.......1......10
...........5.......3.......1.......7.......9
...........6.......4.......1.......5.......6......10
...........7.......1.......1
...........8.......2.......1......10
...........9.......2.......1.......5
..........10.......6.......1.......2.......4.......7.......9......10
MAPLE
seq(seq(seq(`if`(orthopoly[T](k, t)-1 mod j = 0, t, NULL), t=1..j-1), k=1..j-1), j=2..20); # Robert Israel, Apr 06 2015
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Christopher Hunt Gribble, Aug 27 2009
EXTENSIONS
Sequence corrected by Christopher Hunt Gribble, Sep 10 2009
Minor edit by N. J. A. Sloane, Sep 13 2009
Minor edit by Christopher Hunt Gribble, Oct 01 2009
STATUS
approved