OFFSET
1,2
COMMENTS
Geometric interpretation: Consider the two curves y = exp(x) and its inverse y = log(x). They have two shared tangent lines, one with slope b, passing through the kissing points [a,b] and [1/b,-a], the other one with slope 1/b, passing through the kissing points [-a,1/b] and [b,a], where b = exp(a). The values of b and 1/b are reported in A263357.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..2000
FORMULA
Equals log(A263357).
EXAMPLE
1.543404638418208447958709740053315553697883764719262694597241362489...
MATHEMATICA
RealDigits[x/.FindRoot[(x-1)/(x+1) == E^(-x), {x, 1}, WorkingPrecision -> 120], 10, 105][[1]] (* Vaclav Kotesovec, Nov 06 2015 *)
PROG
(PARI) solve(x=0, 10, (x-1)/(x+1)-exp(-x))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Oct 16 2015
STATUS
approved