

A263356


Decimal expansion of the solution of (x1)/(x+1) = exp(x).


2



1, 5, 4, 3, 4, 0, 4, 6, 3, 8, 4, 1, 8, 2, 0, 8, 4, 4, 7, 9, 5, 8, 7, 0, 9, 7, 4, 0, 0, 5, 3, 3, 1, 5, 5, 5, 3, 6, 9, 7, 8, 8, 3, 7, 6, 4, 7, 1, 9, 2, 6, 2, 6, 9, 4, 5, 9, 7, 2, 4, 1, 3, 6, 2, 4, 8, 9, 8, 8, 7, 7, 3, 9, 6, 2, 9, 4, 7, 3, 6, 1, 8, 6, 2, 9, 5
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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[(x1)/(x+1) == E^(x), {x, 1}, WorkingPrecision > 120], 10, 105][[1]] (* Vaclav Kotesovec, Nov 06 2015 *)


PROG

(PARI) solve(x=0, 10, (x1)/(x+1)exp(x))


CROSSREFS

Cf. A263357.
Sequence in context: A132669 A276052 A321028 * A061836 A021188 A334337
Adjacent sequences: A263353 A263354 A263355 * A263357 A263358 A263359


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Oct 16 2015


STATUS

approved



