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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
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.
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
Sequence in context: A307222 A336553 A366460 * A046426 A056776 A172466
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, May 17 2008
STATUS
approved