A236229 Larger of the two real zeros of x - exp(x/(x-1)).

3, 8, 5, 7, 3, 3, 4, 8, 2, 5, 9, 4, 9, 3, 7, 8, 5, 7, 9, 5, 5, 2, 7, 9, 3, 1, 0, 5, 0, 3, 3, 0, 4, 2, 5, 4, 1, 5, 8, 9, 1, 9, 6, 1, 1, 2, 1, 7, 4, 6, 7, 6, 2, 4, 4, 1, 6, 8, 0, 1, 5, 5, 3, 7, 9, 9, 4, 4, 0, 5, 0, 0, 8, 8, 9, 8, 2, 4, 3, 0, 5, 7, 9, 4, 1, 4, 5, 4, 7, 7, 1, 6, 3, 3, 8, 1, 7, 3, 6, 5, 0, 8, 7, 7, 5

Offset

1,1

Comments

The other root (lower value) is given by A236230.

This root can be found by simple recursion on x = exp(x/(x-1)).

The inverse of this number, 0.2592463566483, is the lower value of the two roots of: x - exp(1/(x-1)). This same property, with different values, applies using any base >= 1 for exponentiation, not just for e.

This is also the solution of 1/x + 1/(log x) = 1; see A329977 and A329978 for related Beatty sequences. - Clark Kimberling Jan 02 2020

Links

Table of n, a(n) for n=1..105.

Example

3.85733482594937857...

Mathematica

RealDigits[FindRoot[x - E^(x/(x - 1)), {x, 1.1}, WorkingPrecision -> 105][[1, 2]]][[1]]

Crossrefs

Cf. A236230, A329977, A329978.

Sequence in context: A155676 A200243 A379975 * A343920 A258985 A077151

Adjacent sequences: A236226 A236227 A236228 * A236230 A236231 A236232

Keyword

nonn,cons

Author

Richard R. Forberg, Jan 20 2014

Status

approved