

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 ycoordinate 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
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OFFSET

0,1


LINKS

V. G. Drinfel'd, A cyclic inequality, Mathematical Notes of the Academy of Sciences of the USSR, 9 (1971), 6871.


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))*(1b+c(b))2/(exp(b)+exp(b/2))));
exp(a)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



