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

Author

Mohammad K. Azarian, Mar 27 2004

Keywords

• nonn
• cons

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

Examples

			1.39561242508608952862812531960258683759790651519940...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers

Crossrefs

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

Programs

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 *)

PARI

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

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