|
|
A335339
|
|
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 y-coordinate of the point at which the line touches y = exp(-x).
|
|
2
|
|
|
8, 5, 6, 2, 4, 8, 2, 1, 4, 4, 4, 9, 2, 6, 6, 1, 1, 6, 8, 4, 3, 3, 4, 5, 8, 9, 5, 9, 7, 0, 5, 5, 3, 2, 9, 6, 7, 6, 9, 1, 7, 6, 4, 1, 8, 1, 5, 9, 0, 4, 1, 1, 1, 2, 8, 7, 2, 2, 1, 4, 2, 5, 9, 5, 5, 5, 7, 1, 1, 4, 3, 5, 9, 8, 0, 5, 9, 1, 1, 5, 3, 6, 9, 8, 5, 8, 4, 4, 3, 7, 7, 2
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
V. G. Drinfel'd, A cyclic inequality, Mathematical Notes of the Academy of Sciences of the USSR, 9 (1971), 68-71.
|
|
FORMULA
|
Equals the negative of the slope of the common tangent = -(A335339 - A335245)/(A319569 - (-A319568)) = -(exp(-c) - 2/(exp(b) + exp(b/2))) / (c - b).
|
|
EXAMPLE
|
0.856248214449266116843345...
|
|
PROG
|
(PARI) c(b) = b + exp(b/2)/(2*exp(b)+exp(b/2));
a = c(solve(b=-2, 2, exp(-c(b))*(1-b+c(b))-2/(exp(b)+exp(b/2))));
exp(-a)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|