

A196765


Decimal expansion of the positive number c for which the curve y=c/x is tangent to the curve y=sin(x), and 0 < x < 2*Pi.


8



1, 8, 1, 9, 7, 0, 5, 7, 4, 1, 1, 5, 9, 6, 5, 3, 0, 4, 6, 2, 0, 6, 9, 5, 7, 6, 8, 0, 3, 7, 5, 5, 2, 8, 1, 4, 5, 6, 1, 6, 5, 2, 2, 4, 7, 8, 4, 4, 1, 6, 3, 4, 0, 3, 6, 1, 5, 1, 2, 9, 5, 5, 0, 7, 3, 3, 1, 4, 4, 0, 0, 1, 6, 7, 6, 0, 3, 3, 9, 6, 1, 7, 8, 6, 5, 6, 1, 9, 5, 0, 7, 4, 4, 4, 8, 1, 5, 2, 6, 6, 0, 5, 3, 3, 3
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OFFSET

1,2


COMMENTS

Also, the least local maximum of x*sin(x), which occurs exactly at x = +A196504, where x = +A196504 is the xcoordinate of this point of tangency of c/x and sin(x) in the first quadrant. There also exists a negative constant d such that d/x and sin(x) are tangent in the fourth quadrant for 0 < x < 2*Pi.  Rick L. Shepherd, Jan 12 2014


LINKS

Table of n, a(n) for n=1..105.


EXAMPLE

x=1.8197057411596530462069576803755281456165224784...


MATHEMATICA

Plot[{Sin[x], 1/x, 1.82/x}, {x, 0, Pi}]
xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision > 100]
RealDigits[xt] (* A196504 *)
c = N[xt*Sin[xt], 100]
RealDigits[c] (* A196765 *)
slope = Cos[xt]
RealDigits[slope](* A196766 *)
(* 2nd program for A196765 by Rick L. Shepherd, Jan 12 2014 *)
RealDigits[N[MaxValue[{x*Sin[x], x>1 && x<3}, {x}], 120]]


CROSSREFS

Cf. A196760.
Sequence in context: A021126 A091557 A332079 * A182526 A298519 A238271
Adjacent sequences: A196762 A196763 A196764 * A196766 A196767 A196768


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 06 2011


EXTENSIONS

More terms from Rick L. Shepherd, Jan 12 2014


STATUS

approved



