Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #49 Dec 13 2024 11:21:13
%S 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,
%T 7,8,6,3,5,0,2,8,2,8,0,1,3,6,4,8,8,2,2,8,4,4,3,4,1,6,2,9,2,7,3,5,8,9,
%U 1,7,2,5,0,2,1,4,1,5,0,1,9,5,2,8,7,5,1,9,9,4,2,2,2,5,8,7,8,6,0,4,7,3,5,7,5
%N Decimal expansion of c^c^c^... where c is the constant defined in A037077.
%C See (Weisstein) link on Power Tower.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>.
%H Gus Wiseman, <a href="http://www.nafindix.com/math/math.html">Tetration</a>.
%H OEIS Wiki, <a href="/wiki/Tetration">Tetration</a>.
%H OEIS Wiki, <a href="/wiki/MRB_constant">MRB constant</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration">Tetration</a>.
%e 0.4619214401644114454085886426141945786350282801364882284434162927358917250...
%t n = 105; M = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity}, WorkingPrecision -> n + 10, Method -> "AlternatingSigns"]; L = Log[M]; N[-ProductLog[-L]/L, n] (* _Marvin Ray Burns_, Mar 08 2013 *)
%o (PARI)
%o default(realprecision,66);
%o M=sumalt(x=1,(-1)^x*((x^(1/x))-1));
%o solve(x=.46,.462,x^(1/x)-M)
%Y Cf. A037077, A000027, A000312, A002488, A073230.
%K cons,nonn
%O 0,1
%A _Marvin Ray Burns_ Jan 20 2000, Mar 28 2008, Nov 08 2009, Mar 24 2010, Jun 27 2011
%E Simplified definition by _Marvin Ray Burns_, Mar 08 2013