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A166928 Decimal expansion of smaller solution to 3^x = x^3. 0

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of smaller solution to 3^x = x^3.

%C The larger solution is of course 3.

%C 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

%C The constant is transcendental (Vassilev-Missana, p. 23). - _Peter Bala_, Jan 01 2014

%H M. Vassilev-Missana, <a href="http://nntdm.net/volume-16-2010/number-3/18-24/">Some results on infinite power towers</a>, Notes on Number Theory and Discrete Mathematics, Vol. 16 (2010) No. 3, 18-24.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 2.47805268028830241189373651689...

%t RealDigits[ -3*ProductLog[ -Log[3]/3 ] / Log[3], 10, 105] // First (* _Jean-Fran├žois Alcover_, Mar 05 2013 *)

%o (PARI) solve(x=2,exp(1),3^x-x^3)

%K cons,nonn

%O 1,1

%A _Franklin T. Adams-Watters_, Oct 23 2009

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)