

A140278


Ceiling of the (firstquadrant) angle in degrees whose tangent is n.


2



0, 45, 64, 72, 76, 79, 81, 82, 83, 84, 85, 85, 86, 86, 86, 87, 87, 87, 87, 87, 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, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90
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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 >= 58.


LINKS

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


FORMULA

For all integers n, a(n) = ceiling(180*atan(n)/Pi) = A140276(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(2) = 64 degrees as 180*atan(2)/Pi = 63.4349... and ceiling(63.4349...) = 64.


MATHEMATICA

Ceiling[180*ArcTan[Range[0, 70]]/Pi] (* Harvey P. Dale, Apr 13 2019 *)


PROG

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


CROSSREFS

Cf. A140276, A140277.
Sequence in context: A051773 A307222 A336553 * A046426 A056776 A172466
Adjacent sequences: A140275 A140276 A140277 * A140279 A140280 A140281


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, May 17 2008


STATUS

approved



