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A140278 Ceiling of the (first-quadrant) 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 (list; graph; refs; listen; history; text; internal format)
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 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) = 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

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Last modified November 29 16:39 EST 2022. Contains 358431 sequences. (Running on oeis4.)