OFFSET
0,2
COMMENTS
Tetration is defined recursively: x^^0 = 1, x^^n = x^(x^^(n-1)). Its inverse, super-root, is defined: sr[n](y) = x iff x^^n = y. Note that lim_{n->inf} sr[n](2) = sqrt(2). Asymptotically, sr[n](2) = sqrt(2) + O(log(2)^n). This constant is the coefficient in the O(log(2)^n) term, i.e. lim_{n->inf} (sr[n](2) - sqrt(2))/log(2)^n.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..193
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Super-root
FORMULA
a = A277435*(1-log(2))/(2*sqrt(2)). - Vladimir Reshetnikov, Oct 18 2016
EXAMPLE
0.0685756598113291039765533114155...
MATHEMATICA
{0}~Join~RealDigits[SequenceLimit[1`200 Table[(2 - Power @@ Table[Sqrt[2], {n}])/Log[2]^n, {n, 1, 200}]] (1 - Log[2])/(2 Sqrt[2]), 10, 100][[1]] (* Vladimir Reshetnikov, Oct 18 2016 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Vladimir Reshetnikov, Nov 15 2015
STATUS
approved