A263356 Decimal expansion of the solution of (x-1)/(x+1) = exp(-x).

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

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

Cf. A263357.

Sequence in context: A348340 A321028 A351169 * A061836 A021188 A334337

Adjacent sequences: A263353 A263354 A263355 * A263357 A263358 A263359

Keyword

nonn,cons

Author

Stanislav Sykora, Oct 16 2015

Status

approved