This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A258020 #13 Jun 05 2015 03:51:21 %S A258020 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, %T A258020 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, %U A258020 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 %N 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. %C A258020 Note that this sequence lists such values only for nonnegative integers, although the function is defined in all Z. %H A258020 Antti Karttunen, <a href="/A258020/b258020.txt">Table of n, a(n) for n = 0..10000</a> %F A258020 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.] %e A258020 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. %e A258020 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. %o A258020 (Scheme) (define (A258020 n) (if (= n (floor->exact (tan n))) 0 (+ 1 (A258020 (floor->exact (tan n)))))) %Y A258020 Cf. A000503, A258021, A258022, A258024, A258201. %K A258020 nonn %O A258020 0,3 %A A258020 _Antti Karttunen_, May 24 2015