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 A140276 Floor of the (first-quadrant) angle in degrees whose tangent is n. 2

%I

%S 0,45,63,71,75,78,80,81,82,83,84,84,85,85,85,86,86,86,86,86,87,87,87,

%T 87,87,87,87,87,87,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,88,

%U 88,88,88,88,88,88,88,88,88,88,88,88,89,89,89,89,89,89,89,89,89,89,89,89

%N Floor of the (first-quadrant) angle in degrees whose tangent is n.

%C 180*atan(n)/Pi is an exact integer only for n = 0 and n = 1 (and n = -1). a(n) = 89 for n >= 58.

%F For all integers n, a(n) = floor(180*atan(n)/Pi) = -A140278(-n), where a negative term represents a fourth-quadrant angle. Terms shown are only for n >= 0.

%e a(1) = 45 degrees as that is the first-quadrant angle with tan(45 deg) = 1. a(2) = 63 degrees as 180*atan(2)/Pi = 63.4349... and floor(63.4349...) = 63.

%o (PARI) a(n) = floor(180*atan(n)/Pi)

%Y Cf. A140277, A140278.

%K nonn

%O 0,2

%A _Rick L. Shepherd_, May 16 2008

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