A260691 Decimal expansion of a constant related to asymptotic behavior of super-roots of 2: lim_{n->inf} (sr[n](2) - sqrt(2))/log(2)^n.

0, 6, 8, 5, 7, 5, 6, 5, 9, 8, 1, 1, 3, 2, 9, 1, 0, 3, 9, 7, 6, 5, 5, 3, 3, 1, 1, 4, 1, 5, 5, 0, 6, 5, 5, 4, 2, 3, 3, 5, 6, 3, 5, 7, 1, 3, 7, 8, 6, 1, 9, 4, 4, 7, 4, 6, 8, 1, 2, 5, 1, 7, 0, 5, 1, 0, 3, 4, 8, 4, 4, 6, 8, 0, 7, 3, 4, 9, 7, 3, 7, 7, 4, 6, 0, 7, 1, 7, 1, 4, 3, 0, 9, 3, 0, 8, 1, 9, 7, 9, 1, 1, 1, 3, 9, 7, 4, 2, 8, 6

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

Cf. A198094, A277435.

Sequence in context: A296426 A249282 A289090 * A296845 A030644 A319032

Adjacent sequences: A260688 A260689 A260690 * A260692 A260693 A260694

Keyword

cons,nonn

Author

Vladimir Reshetnikov, Nov 15 2015

Status

approved