A092041 Decimal expansion of cube root of e.

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

Offset

1,2

Comments

e^(1/3) maximizes the value of x^(c/(x^3)) for any real positive constant c, and minimizes for it for a negative constant, on the range x > 0. - A.H.M. Smeets, Aug 16 2018

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for transcendental numbers

Formula

Equals (729/1552)*(1 + Sum_{n>=1} (1 + n^5/3 + n/3)/(3^n*n!)). - Alexander R. Povolotsky, Sep 13 2011

Equals (1/2)*(1 + (4 + (7 + (10 + ...)/9)/6)/3) = 1 + (1 + (1 + (1 + ...)/9)/6)/3. - Rok Cestnik, Jan 19 2017

Equals lim_{x->0} (tan(x)/x)^(1/x^2). - Amiram Eldar, Jul 04 2022

Example

1.39561242508608952862812531960258683759790651519940...

Maple

evalf(root[3](exp(1))) ; # R. J. Mathar, Oct 03 2011

Mathematica

RealDigits[E^(1/3), 10, 100][[1]] (* Alonso del Arte, Sep 13 2011 *)

Prog

(PARI) exp(1/3) \\ Charles R Greathouse IV, Sep 14 2011

Crossrefs

Cf. A001113, A019774, A091933, A092615 (reciprocal).

Sequence in context: A373099 A212321 A306552 * A317904 A320960 A193075

Adjacent sequences: A092038 A092039 A092040 * A092042 A092043 A092044

Keyword

nonn,cons

Author

Mohammad K. Azarian, Mar 27 2004

Status

approved