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 A073229 Decimal expansion of e^(1/e). 25
 1, 4, 4, 4, 6, 6, 7, 8, 6, 1, 0, 0, 9, 7, 6, 6, 1, 3, 3, 6, 5, 8, 3, 3, 9, 1, 0, 8, 5, 9, 6, 4, 3, 0, 2, 2, 3, 0, 5, 8, 5, 9, 5, 4, 5, 3, 2, 4, 2, 2, 5, 3, 1, 6, 5, 8, 2, 0, 5, 2, 2, 6, 6, 4, 3, 0, 3, 8, 5, 4, 9, 3, 7, 7, 1, 8, 6, 1, 4, 5, 0, 5, 5, 7, 3, 5, 8, 2, 9, 2, 3, 0, 4, 7, 0, 9, 8, 8, 5, 1, 1, 4, 2, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS e^(1/e) = 1/((1/e)^(1/e)) (reciprocal of A072364). Let w(n+1)=A^w(n); then w(n) converges if and only if (1/e)^e <= A <= e^(1/e) (see the comments in A073230) for initial value w(1)=A. If A=e^(1/e) then lim_{n->infinity} w(n) = e. - Benoit Cloitre, Aug 06 2002; corrected by Robert FERREOL, Jun 12 2015 x^(1/x) is maximum for x = e and the maximum value is e^(1/e). This gives an interesting and direct proof that 2 < e < 4 as 2^(1/2) < e^(1/e) > 4^(1/4) while 2^(1/2) = 4^(1/4). - Amarnath Murthy, Nov 26 2002 For large n, A234604(n)/A234604(n-1) converges to e^(1/e). - Richard R. Forberg, Dec 28 2013 Value of the unique base b > 0 for which the exponential curve y=b^x and its inverse y=log_b(x) kiss each other; the kissing point is (e,e). - Stanislav Sykora, May 25 2015 Actually, there is another base with such property, b=(1/e)^e with kiss point (1/e,1/e). - Yuval Paz, Dec 29 2018 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Simon Plouffe, exp(1/e) J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see Definition 4.1 on p. 158. Eric Weisstein's World of Mathematics, Steiner's Problem FORMULA Equals 1 + Integral_{x = 1/e..1} (1 + log(x))/x^x dx = 1 - Integral_{x = 0..1/e} (1 + log(x))/x^x dx. - Peter Bala, Oct 30 2019 Equals Sum_{k>=0} exp(-k)/k!. - Amiram Eldar, Aug 13 2020 EXAMPLE 1.44466786100976613365833910859... MAPLE evalf(exp(exp(-1))); # Muniru A Asiru, Dec 29 2018 MATHEMATICA RealDigits[ E^(1/E), 10, 110] [] PROG (PARI) exp(1)^exp(-1) CROSSREFS Cf. A001113 (e), A068985 (1/e), A073230 ((1/e)^e), A072364 ((1/e)^(1/e)), A073226 (e^e). Sequence in context: A114742 A273909 A098013 * A116446 A102126 A277433 Adjacent sequences:  A073226 A073227 A073228 * A073230 A073231 A073232 KEYWORD cons,nonn AUTHOR Rick L. Shepherd, Jul 22 2002 STATUS approved

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Last modified September 18 05:36 EDT 2020. Contains 337166 sequences. (Running on oeis4.)