A052110 - OEIS

%I #50 Feb 16 2025 08:32:41

%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="https://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,changed

%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