OFFSET
0,3
COMMENTS
Note that this sequence lists such values only for nonnegative integers, although the function is defined in all Z.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..10000
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.]
EXAMPLE
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.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 24 2015
STATUS
approved