A164846 Triangle read by rows: frequency with which the number of values taken by cos(2*Pi/k) mod j occurs for each j >= 1, taken over k = 1..j-1.

0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 3, 0, 0, 0, 3, 0, 0, 1, 1, 0, 2, 3, 0, 1, 0, 0, 0, 4, 0, 0, 2, 0, 0, 1, 0, 3, 1, 1, 2, 0, 1, 0, 0, 0, 3, 2, 0, 1, 2, 0, 0, 1, 0, 0, 2, 5, 1, 1, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 3, 6, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 5, 2, 0, 2, 1, 0, 0, 1, 2, 0, 0, 0, 0

Offset

1,8

Comments

See A164823 for explanatory comment and the definition of "cos(x) mod j".

Links

Christopher Hunt Gribble, Flattened triangle, for j = 1..100 and k = 1..j-1.

Example

The triangle of numbers is:
..j....Frequency of numbers of solutions over k
.......0..1..2..3..4..5..6..7..8..9..10
..1....0
..2....0..1
..3....0..1..1
..4....0..2..1..0
..5....0..1..3..0..0
..6....0..3..0..0..1..1
..7....0..2..3..0..1..0..0
..8....0..4..0..0..2..0..0..1
..9....0..3..1..1..2..0..1..0..0
.10....0..3..2..0..1..2..0..0..1..0
.11....0..2..5..1..1..0..1..0..0..0..0

Crossrefs

Cf. A164822, A164823, A164831, A165252.

Sequence in context: A337126 A319572 A108063 * A363928 A331385 A026729

Adjacent sequences: A164843 A164844 A164845 * A164847 A164848 A164849

Keyword

nonn,tabl

Author

Christopher Hunt Gribble, Aug 28 2009

Extensions

Minor edits from N. J. A. Sloane, Sep 01 2009

Sequence corrected by Christopher Hunt Gribble, Sep 10 2009

Minor edits by Christopher Hunt Gribble, Oct 01 2009

Status

approved