A258021 Eventual fixed point of map x -> floor(tan(x)) when starting the iteration with the initial value x = n.

0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0

Offset

0

Comments

Note that this sequence lists the terminating values only for the nonnegative starting points of the iteration map, although the function is defined in all Z and the intermediate steps in iteration may visit also negative numbers.

Pohjola conjectures that no other numbers than 0 and 1 will ever occur in this sequence.

In any case, any strictly positive term present in this sequence must be one of the terms of A249836.

Links

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

Formula

If n is equal to floor(tan(n)), then a(n) = n, and for any other n (positive or negative), a(n) = a(floor(tan(n))). [Recurrence defined in whole Z.]

Prog

(Scheme) (define (A258021 n) (if (= n (floor->exact (tan n))) n (A258021 (floor->exact (tan n)))))

Crossrefs

Cf. A000503, A258020, A258202, A249836.

Cf. also A258022 (positions of terms <= 0), A258024 (positions of terms >= 1), A258201 (the smallest number visited in the iteration).

Sequence in context: A356921 A356922 A106701 * A033684 A080885 A258998

Adjacent sequences: A258018 A258019 A258020 * A258022 A258023 A258024

Keyword

nonn

Author

V.J. Pohjola & Antti Karttunen, May 24 2015

Status

approved