%I A052110
%S A052110 4,6,1,9,2,1,4,4,0,1,6,4,4,1,1,4,4,5,4,0,8,5,8,8,6,4,2,6,1,4,1,9,4,5,7,
%T A052110 8,6,3,5,0,2,8,2,8,0,1,3,6,4,8,8,2,2,8,4,4,3,4,1,6,2,9,2,7,3,5,8,9,1,7,
%U A052110 2,5,0,2,1,4,1,5,0,1,9,5,2,8,7,5,1,9,9,4,2,2,2,5,8,7,8,6,0,4,7,3,5,7,5
%N A052110 Decimal expansion of limit c^c^c^c... (with an even number of terms) 
               where c is the constant defined in A037077.
%C A052110 In fact, since the alternating sum in A037077 converges to two sums differing 
               by 1, there are three products produced by c^c^c^... . All three 
               results are shown in the Mathematica program below.
%D A052110 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.
%H A052110 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/itrexp/itrexp.html">
               Iterated Exponential Constants</a>
%H A052110 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PowerTower.html">Link to a section of The World of Mathematics</a>
%H A052110 Gus Wiseman, <a href="http://www.nafindix.com/math/math.html">Tetration</
               a>
%H A052110 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration">Tetrations</
               a>
%t A052110 PowerTower[x_, n_ ] := Nest[Power[x, # ] &, x, n - 1 ]; m = NSum[(-1)^n*(n^(1/
               n) - 1), {n, Infinity}, WorkingPrecision -> 100, Method -> "AlternatingSigns" 
               ]; N[PowerTower[m, 860 ], 100 ]
%o A052110 (PARI) c=sumalt(x=1,(-1)^x*((x^(1/x))-1)):solve(x=.46,.462,x^(1/x)-c)
%Y A052110 Cf. A037077.
%Y A052110 Cf. A000027, A000312, A002488, A073230 .
%Y A052110 Sequence in context: A051261 A030169 A156789 this_sequence A131701 A021688 
               A119439
%Y A052110 Adjacent sequences: A052107 A052108 A052109 this_sequence A052111 A052112 
               A052113
%K A052110 cons,nonn,new
%O A052110 0,1
%A A052110 Marvin Ray Burns (bmmmburns(AT)sbcglobal.net) Jan 20 2000, Mar 28 2008, 
               Nov 08 2009