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A166928
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Decimal expansion of smaller solution to 3^x = x^3.
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1
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2, 4, 7, 8, 0, 5, 2, 6, 8, 0, 2, 8, 8, 3, 0, 2, 4, 1, 1, 8, 9, 3, 7, 3, 6, 5, 1, 6, 8, 9, 4, 6, 9, 0, 3, 0, 7, 8, 6, 8, 1, 4, 2, 3, 1, 2, 6, 8, 9, 0, 9, 9, 1, 6, 3, 5, 9, 1, 2, 6, 3, 8, 1, 0, 0, 8, 7, 1, 1, 2, 5, 2, 2, 1, 6, 7, 0, 1, 4, 6, 4, 0, 5, 1, 4, 7, 3, 2, 1, 8, 3, 4, 8, 6, 9, 3, 6, 6, 9, 3, 6, 9, 2, 0, 1
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OFFSET
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1,1
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COMMENTS
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The larger solution is of course 3.
Also, the limit of infinite tetration a^a^...^a of a=3^(1/3) (=A002581), i.e., lim_{n->oo} x(n) where x(n+1)=a^x(n), x(1)=a. - M. F. Hasler, Nov 03 2013
The constant is transcendental (Vassilev-Missana, p. 23). - Peter Bala, Jan 01 2014
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LINKS
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EXAMPLE
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2.47805268028830241189373651689...
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MATHEMATICA
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RealDigits[ -3*ProductLog[ -Log[3]/3 ] / Log[3], 10, 105] // First (* Jean-François Alcover, Mar 05 2013 *)
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PROG
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(PARI) solve(x=2, exp(1), 3^x-x^3)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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