A165619 a(n) = number of nonexistent values of cos(2*Pi/k) mod n, taken over k = 1..n-1.

0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 3, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 6, 0, 10, 0, 0, 0, 8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 8, 0, 15, 0, 0, 0, 0, 0, 16, 0, 0, 0, 12, 0, 18, 0, 0, 0, 0, 0, 16, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 16

Offset

1,7

Comments

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

It appears that a(n) = 0 for all n >= 1 other than n = 4 and n = any prime >= 5. Also, a(n) is even for all primes of the form 4m+3, with m >= 1, since, referring to the triangle in A165609, if c mod n is nonexistent then so is -c mod n.

Links

Christopher Hunt Gribble, Table of n, a(n) for n = 1..1000.

Crossrefs

Cf. A164823, A165609.

Sequence in context: A097106 A175801 A361250 * A368118 A328590 A219204

Adjacent sequences: A165616 A165617 A165618 * A165620 A165621 A165622

Keyword

nonn

Author

Christopher Hunt Gribble, Sep 22 2009

Extensions

Comment corrected by Christopher Hunt Gribble, Sep 25 2009

Status

approved