A092514 Decimal expansion of e^(1/5).

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

Offset: 1

Author

Mohammad K. Azarian, Apr 05 2004

Keywords

• cons
• nonn

Comments

e^(1/5) maximizes the value of x^(c/(x^5)) 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

			1.22140275816...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for transcendental numbers

Crossrefs

Cf. A001113, A019774.

Programs

Magma

Exp(1/5); // Vincenzo Librandi, Aug 17 2018

Maple

evalf(exp(1/5)); # Muniru A Asiru, Aug 16 2018

Mathematica

RealDigits[Surd[E,5],10,120][[1]] (* Harvey P. Dale, Aug 12 2016 *)

PARI

exp(1/5) \\ Michel Marcus, Aug 16 2018

Formula

e^(1/5) = 5^(2*5)/21355775*(1 + Sum_{n>=1} (1 + n^7/5 + n/5)/(5^n*n!)). - Alexander R. Povolotsky, Sep 13 2011

e^(1/5) = (1/2)*lim_{n -> oo} 1 + (6 + (11 + (16 + ... + ((5*n+1)/ (5*n))/...)/15)/10)/5 = lim_{n -> oo} 1 + (1 + (1 + (1 + ... + (1 + 1/(5*n+5))/(5*n)/...)/15)/10)/5. - Rok Cestnik, Jan 19 2017