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A176360 a(n) = quadrant of unit circle corresponding to n radians. 0

%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

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Last modified September 24 15:14 EDT 2020. Contains 337321 sequences. (Running on oeis4.)