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A073229
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Decimal expansion of e^(1/e).
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17
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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; internal format)
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OFFSET
| 1,2
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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 any initial value w(1)>0. If A=e^(1/e) then lim n -> infinity w(n) = e. - Benoit Cloitre, Aug 06 2002
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 (amarnath_murthy(AT)yahoo.com), Nov 26 2002
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LINKS
| 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
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EXAMPLE
| 1.44466786100976613365833910859...
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MATHEMATICA
| RealDigits[ E^(1/E), 10, 110] [[1]]
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PROG
| (PARI) exp(1)^exp(-1)
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CROSSREFS
| Cf. A001113 (e), A068985 (1/e), A073230 ((1/e)^e), A072364 ((1/e)^(1/e)), A073226 (e^e).
Sequence in context: A114742 A098013 A116446 * A102126 A097918 A141466
Adjacent sequences: A073226 A073227 A073228 * A073230 A073231 A073232
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KEYWORD
| cons,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 22 2002
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