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A319569 Given the two curves y = exp(-x) and y = 2/(exp(x) + exp(x/2)), draw a line tangent to both. This sequence is the decimal expansion of the x-coordinate of the point at which the line touches y = exp(-x). 1
1, 5, 5, 1, 9, 4, 9, 7, 4, 7, 2, 2, 6, 0, 1, 9, 8, 1, 1, 0, 3, 7, 1, 7, 4, 2, 9, 5, 6, 2, 8, 3, 9, 3, 8, 3, 6, 6, 0, 6, 0, 4, 3, 2, 4, 9, 0, 9, 6, 6, 7, 7, 4, 0, 4, 2, 8, 9, 3, 8, 2, 4, 8, 0, 9, 6, 0, 7, 3, 2, 7, 3, 6, 7, 5, 0, 2, 0, 3, 9, 1, 3, 6, 6, 6, 2, 7, 2, 7, 4, 2, 4, 9, 3, 9, 9, 8, 1, 2, 2, 9, 2, 0, 8, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..105.

Eric Weisstein's MathWorld, Shapiro's Cyclic Sum Constant

FORMULA

b = -0.2008110658618... (A319568).

c =  0.1551949747226... .

1 - b + c = 2*exp(c)/(exp(b) + exp(b/2)).

exp(-c) * (c + 1) = 0.989133634446... (phi(0)).

Equals -1 - LambertW(-1, -exp(-1)*A245330). - Vaclav Kotesovec, Sep 26 2018

EXAMPLE

0.1551949747226...

CROSSREFS

Cf. A245330 (phi(0)), A319568.

Sequence in context: A300710 A254347 A011094 * A204005 A075298 A060058

Adjacent sequences:  A319566 A319567 A319568 * A319570 A319571 A319572

KEYWORD

nonn,cons

AUTHOR

Seiichi Manyama, Sep 23 2018

EXTENSIONS

More terms from Vaclav Kotesovec, Sep 26 2018

STATUS

approved

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Last modified February 27 18:19 EST 2020. Contains 332307 sequences. (Running on oeis4.)