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A140278
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Ceiling of the (first-quadrant) angle in degrees whose tangent is n.
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2
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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
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0,2
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COMMENTS
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180*atan(n)/Pi is an exact integer only for n = 0 and n = 1 (and n = -1).
a(n) = 90 for n >= 58.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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MATHEMATICA
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Ceiling[180*ArcTan[Range[0, 70]]/Pi] (* Harvey P. Dale, Apr 13 2019 *)
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PROG
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(PARI) a(n) = ceil(180*atan(n)/Pi)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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