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 A140277 Rounded (first-quadrant) 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 (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 >= 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 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 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(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

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Last modified October 17 19:24 EDT 2019. Contains 328127 sequences. (Running on oeis4.)