A140277 Rounded (first-quadrant) angle in degrees whose tangent is n.

0, 45, 63, 72, 76, 79, 81, 82, 83, 84, 84, 85, 85, 86, 86, 86, 86, 87, 87, 87, 87, 87, 87, 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, 89, 89, 89, 89, 89, 89, 89, 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) = 90 for n >= 115.

Also, for n>0, rounded value of the angle at O=(0,0) of a triangle OPQ with P=(n,0) and Q=(n,n^2). - M. F. Hasler, Oct 07 2012

Links

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

Project Euler, Problem 397: Triangle on parabola, Oct 07 2012.

Formula

For all integers n, a(n) = round(180*atan(n)/Pi) = -a(-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(3) = 72 degrees as 180*atan(3)/Pi = 71.5650... and 71.5650... rounded to the nearest integer is 72. (Method is .5000... rounds up.)

Prog

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

Crossrefs

Cf. A140276, A140278.

Sequence in context: A138046 A324367 A140276 * A242263 A242264 A333326

Adjacent sequences: A140274 A140275 A140276 * A140278 A140279 A140280

Keyword

nonn

Author

Rick L. Shepherd, May 16 2008

Status

approved