A387101 Decimal expansion of the smallest real solution to e^x = x^3.

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

Offset

1,2

Comments

Equivalently, the smallest real solution to log(x) = x/3.

Links

Table of n, a(n) for n=1..100.

Index entries for transcendental numbers.

Formula

Equals -3*LambertW(-1/3).

Example

1.85718386020783533645698098206276669990441533...

Mathematica

RealDigits[-3*ProductLog[-1/3], 10, 100][[1]]
RealDigits[x/.FindRoot[E^x==x^3, {x, 1}, WorkingPrecision->120], 10, 120][[1]] (* Harvey P. Dale, Sep 02 2025 *)

Prog

(PARI) -3*lambertw(-1/3) \\ Michel Marcus, Aug 18 2025

Crossrefs

Cf. A030178, A126583, A126584, A387102 (largest).

Sequence in context: A020786 A304226 A019868 * A121472 A117039 A327949

Adjacent sequences: A387098 A387099 A387100 * A387102 A387103 A387104

Keyword

nonn,cons

Author

Stefano Spezia, Aug 16 2025

Status

approved