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%I #45 Oct 02 2022 23:09:21
%S 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,
%T 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,
%U 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
%N Decimal expansion of cube root of e.
%C 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
%H G. C. Greubel, <a href="/A092041/b092041.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals (729/1552)*(1 + Sum_{n>=1} (1 + n^5/3 + n/3)/(3^n*n!)). - _Alexander R. Povolotsky_, Sep 13 2011
%F Equals (1/2)*(1 + (4 + (7 + (10 + ...)/9)/6)/3) = 1 + (1 + (1 + (1 + ...)/9)/6)/3. - _Rok Cestnik_, Jan 19 2017
%F Equals lim_{x->0} (tan(x)/x)^(1/x^2). - _Amiram Eldar_, Jul 04 2022
%e 1.39561242508608952862812531960258683759790651519940...
%p evalf(root[3](exp(1))) ; # _R. J. Mathar_, Oct 03 2011
%t RealDigits[E^(1/3), 10, 100][[1]] (* _Alonso del Arte_, Sep 13 2011 *)
%o (PARI) exp(1/3) \\ _Charles R Greathouse IV_, Sep 14 2011
%Y Cf. A001113, A019774, A091933, A092615 (reciprocal).
%K nonn,cons
%O 1,2
%A _Mohammad K. Azarian_, Mar 27 2004
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