

A140277


Rounded (firstquadrant) angle in degrees whose tangent is n.


2



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
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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 fourthquadrant angle. Terms shown are only for n >= 0.


EXAMPLE

a(1) = 45 degrees as that is the firstquadrant 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 A077646
Adjacent sequences: A140274 A140275 A140276 * A140278 A140279 A140280


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, May 16 2008


STATUS

approved



