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

0, 45, 63, 71, 75, 78, 80, 81, 82, 83, 84, 84, 85, 85, 85, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..69.

Formula

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.

Example

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.

Prog

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

Crossrefs

Cf. A140277, A140278.

Sequence in context: A179007 A138046 A324367 * A140277 A242263 A242264

Adjacent sequences: A140273 A140274 A140275 * A140277 A140278 A140279

Keyword

nonn

Author

Rick L. Shepherd, May 16 2008

Status

approved