A236230 Smaller of the two real zeros of x - exp(x/(x-1)).

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

Offset

0,1

Comments

The other root (higher value) is given by A236229.

This root cannot be found by simple recursion on x = exp(x/(x-1)), nor on x = (x-1)*log(x).

The inverse of this number, 2.2399778876565, is the upper 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 root can be found by simple recursion on x = 1/(log(x)-1) + 1. - Jon E. Schoenfield, Feb 03 2014

Links

Table of n, a(n) for n=0..106.

Example

0.4464329784282...

Mathematica

RealDigits[FindRoot[x - E^(x/(x - 1)), {x, 0.1}, WorkingPrecision -> 110][[1, 2]]][[1]]

Crossrefs

Cf. A236229.

Sequence in context: A155976 A284693 A021228 * A195781 A059656 A205373

Adjacent sequences: A236227 A236228 A236229 * A236231 A236232 A236233

Keyword

nonn,cons

Author

Richard R. Forberg, Jan 20 2014

Status

approved