A176360 a(n) = quadrant of unit circle corresponding to n radians.

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, 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, 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

Offset: 1

Author

Adam Helman, Apr 15 2010, Apr 20 2010

Keywords

• nonn
• easy

Comments

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.

Thereby it is "interesting" to consider which quadrant contains successively larger integer radian measure.

Examples

			a(11) is very nearly 7 quadrants as Pi is nearly exactly 22/7.
Indeed, 11 radians lies just 4.4 milliradian (0.25 degree) within the 4th quadrant.
		

Programs

End

Mathematica

Table[Mod[1+Floor[(2n)/Pi],4],{n,120}]/.(0->4) (* Harvey P. Dale, Apr 09 2020 *)

Other

# a(n) = 1 + {floor [2*n/pi] modulo(4)}
# Ruby code by Andy Martin
# Overkill here, 4 places properly gives first 200 terms.
t = 2000000000000000000000000000000000000000000000000000000000000000000
pi = 3141592653589793238462643383279502884197169399375105820974944592307
(1..200).each{ |n| print "#{1 + ((n*t)/pi)%4},"}
print "\b \n"

Formula

a(n) = 1 + {floor [2*n/Pi] modulo(4)}. - Adam Helman, Apr 20 2010