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A073226
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Decimal expansion of e^e.
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22
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1, 5, 1, 5, 4, 2, 6, 2, 2, 4, 1, 4, 7, 9, 2, 6, 4, 1, 8, 9, 7, 6, 0, 4, 3, 0, 2, 7, 2, 6, 2, 9, 9, 1, 1, 9, 0, 5, 5, 2, 8, 5, 4, 8, 5, 3, 6, 8, 5, 6, 1, 3, 9, 7, 6, 9, 1, 4, 0, 7, 4, 6, 4, 0, 5, 9, 1, 4, 8, 3, 0, 9, 7, 3, 7, 3, 0, 9, 3, 4, 4, 3, 2, 6, 0, 8, 4, 5, 6, 9, 6, 8, 3, 5, 7, 8, 7, 3, 4, 6, 0, 5, 1, 1, 5
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Given z > 0, there exist positive real numbers x < y, with x^y = y^x = z, if and only if z > e^e. In that case, 1 < x < e < y and (x,y) = ((1 + 1/t)^t,(1 + 1/t)^(t+1)) for some t > 0. (For example, t = 1 gives 2^4 = 4^2 = 16 > e^e.) Proofs of these classical results and applications of them are in Sondow and Marques (2010).
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REFERENCES
| J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=2,...,20000
Simon Plouffe, exp(E) to 2000 places
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations
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EXAMPLE
| =15.154262241479264189760430272629911905528548536856139769140746405914830973730934...
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MATHEMATICA
| RealDigits[ E^E, 10, 110] [[1]]
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PROG
| (PARI) exp(exp(1))
(PARI) { default(realprecision, 20080); x=exp(1)^exp(1)/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b073226.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 30 2009]
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CROSSREFS
| Cf. A073233 (Pi^Pi), A049006 (i^i), A001113 (e), A073227 (e^e^e), A004002 (Benford numbers), A056072 (floor(e^e^...^e), n e's), A072364 ((1/e)^(1/e)), A030178 (limit of (1/e)^(1/e)^...^(1/e)), A073229 (e^(1/e)), A073230 ((1/e)^e).
Sequence in context: A055191 A060186 A122002 * A021198 A143969 A198366
Adjacent sequences: A073223 A073224 A073225 * A073227 A073228 A073229
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KEYWORD
| cons,nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 21 2002
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EXTENSIONS
| Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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