%I
%S 1,2,2,3,4,4,1,2,2,3,4,4,1,1,2,3,3,4,1,1,2,3,3,4,4,1,2,2,3,4,4,1,2,2,
%T 3,3,4,1,1,2,3,3,4,1,1,2,2,3,4,4,1,2,2,3,4,4,1,1,2,3,3,4,1,1,2,3,3,4,
%U 4,1,2,2,3,4,4,1,2,2,3,3,4,1,1,2,3,3,4,1,1,2,2,3,4,4,1,2,2,3,4,4,1,1,2,3,3
%N a(n) = quadrant of unit circle corresponding to n radians.
%C Radians are the natural measure of angle. Quadrants (1 through 4) determine the signs of (x,y); of (cos x, sin x); and are ubiquitous.
%C Thereby it is "interesting" to consider which quadrant contains successively larger integer radian measure.
%F a(n) = 1 + {floor [2*n/Pi] modulo(4)}.  _Adam Helman_, Apr 20 2010
%e a(11) is very nearly 7 quadrants as Pi is nearly exactly 22/7.
%e Indeed, 11 radians lies just 4.4 milliradian (0.25 degree) within the 4th quadrant.
%t Table[Mod[1+Floor[(2n)/Pi],4],{n,120}]/.(0>4) (* _Harvey P. Dale_, Apr 09 2020 *)
%o From _Adam Helman_, Apr 20 2010: (Start)
%o (Other) # a(n) = 1 + {floor [2*n/pi] modulo(4)}
%o # Ruby code by Andy Martin
%o # Overkill here, 4 places properly gives first 200 terms.
%o t = 2000000000000000000000000000000000000000000000000000000000000000000
%o pi = 3141592653589793238462643383279502884197169399375105820974944592307
%o (1..200).each{ n print "#{1 + ((n*t)/pi)%4},"}
%o print "\b \n"
%o (End)
%K nonn,easy
%O 1,2
%A _Adam Helman_, Apr 15 2010, Apr 20 2010
