A258020 Number of steps to reach a fixed point with map x -> floor(tan(x)) when starting the iteration with the initial value x = n.

0, 0, 2, 5, 1, 5, 5, 1, 6, 5, 1, 2, 5, 1, 2, 5, 1, 6, 4, 1, 3, 4, 1, 1, 2, 5, 1, 5, 5, 1, 6, 5, 1, 6, 5, 1, 2, 5, 1, 6, 4, 1, 3, 4, 1, 1, 2, 5, 1, 5, 5, 1, 6, 5, 1, 4, 5, 1, 7, 5, 1, 6, 4, 1, 3, 4, 1, 1, 2, 5, 1, 5, 5, 1, 2, 5, 1, 7, 5, 1, 6, 5, 1, 6, 4, 1, 3, 4, 1, 1, 4, 5, 1, 2, 5, 1, 2, 5, 1, 5, 5, 1, 6, 5, 1, 2, 4, 1, 3, 4, 1, 1, 4, 5, 1, 2, 5, 1, 2, 5, 1

Offset: 0

Author

Antti Karttunen, May 24 2015

Keywords

• nonn

Comments

Note that this sequence lists such values only for nonnegative integers, although the function is defined in all Z.

Examples

			The only known fixed points of function x -> floor(tan(x)) are 0 and 1 (and it is conjectured there are no others), thus a(0) = a(1) = 0.
For n=2, we get tan(2) = -2.185, thus floor(tan(2)) = -3. tan(-3) = 0.1425, thus floor(tan(-3)) = 0, and we have reached a fixed point in two steps, thus a(2) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000503, A258021, A258022, A258024, A258201.

Programs

Scheme

(define (A258020 n) (if (= n (floor->exact (tan n))) 0 (+ 1 (A258020 (floor->exact (tan n))))))

Formula

If n is equal to floor(tan(n)) then a(n) = 0; for any other n (positive or negative): a(n) = 1 + a(floor(tan(n))). [The domain of the recurrence is whole Z.]