A166928 - OEIS

A166928

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

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

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..105.

M. Vassilev-Missana, Some results on infinite power towers, Notes on Number Theory and Discrete Mathematics, Vol. 16 (2010) No. 3, 18-24.

Index entries for transcendental numbers

EXAMPLE

2.47805268028830241189373651689...

MATHEMATICA

RealDigits[ -3*ProductLog[ -Log[3]/3 ] / Log[3], 10, 105] // First (* Jean-François Alcover, Mar 05 2013 *)

PROG

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

CROSSREFS