cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A166928 #27 Aug 16 2025 03:49:46
%S A166928 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 A166928 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 A166928 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 A166928 Decimal expansion of smaller solution to 3^x = x^3.
%C A166928 The larger solution is of course 3.
%C A166928 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 A166928 The constant is transcendental (Vassilev-Missana, p. 23). - _Peter Bala_, Jan 01 2014
%H A166928 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 A166928 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A166928 2.47805268028830241189373651689...
%t A166928 RealDigits[ -3*ProductLog[ -Log[3]/3 ] / Log[3], 10, 105] // First (* _Jean-François Alcover_, Mar 05 2013 *)
%o A166928 (PARI) solve(x=2,exp(1),3^x-x^3)
%Y A166928 Cf. A073084, A341328.
%K A166928 cons,nonn
%O A166928 1,1
%A A166928 _Franklin T. Adams-Watters_, Oct 23 2009