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A196619 Decimal expansion of the number c for which the curve y=cos(x) is tangent to the curve y=(1/x)-c, and 0<x<2*Pi. 5
4, 5, 4, 4, 5, 1, 8, 6, 6, 3, 5, 4, 2, 2, 6, 5, 9, 9, 8, 1, 9, 6, 9, 1, 1, 4, 6, 3, 2, 9, 5, 2, 3, 4, 0, 2, 8, 3, 6, 3, 4, 6, 9, 6, 1, 1, 7, 9, 5, 6, 7, 2, 2, 1, 8, 1, 1, 7, 2, 6, 3, 4, 1, 4, 5, 1, 2, 5, 7, 1, 7, 1, 7, 6, 6, 8, 0, 0, 5, 9, 9, 3, 4, 9, 4, 8, 5, 0, 9, 9, 7, 9, 0, 1, 6, 0, 2, 7, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
EXAMPLE
x = 0.454451866354226599819691146329523402836346961...
MATHEMATICA
Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
RealDigits[xt] (* A196617 *)
Cos[xt]
RealDigits[Cos[xt]] (* A196618 *)
c = N[1/xt - Cos[xt], 100]
RealDigits[c] (* A196619 *)
slope = -Sin[xt]
RealDigits[slope] (* A196620 *)
PROG
(PARI) a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); 1/x - cos(x) \\ G. C. Greubel, Aug 22 2018
CROSSREFS
Sequence in context: A036444 A329505 A125583 * A343954 A063694 A242624
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 05 2011
STATUS
approved

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Last modified March 29 01:34 EDT 2024. Contains 371264 sequences. (Running on oeis4.)