A277435 Decimal expansion of lim_{n->inf} (2 - sqrt(2)^^n)/log(2)^n, where x^^n denotes tetration.

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

Offset

0,1

Comments

Tetration x^^n is defined recursively: x^^0 = 1, x^^n = x^(x^^(n-1)). Note that sqrt(2)^^inf = lim_{n->inf} sqrt(2)^^n = 2. Asymptotically, sqrt(2)^^n = 2 - O(log(2)^n). This constant is the coefficient in the O(log(2)^n) term. Furthermore, sqrt(2)^^n = 2 - a*log(2)^n + (a^2/(4*(1 - 1/log(2))))*log(2)^(2*n) + O(log(2)^(3*n)).

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Tetration

Formula

a = 2*sqrt(2)*A260691/(1-log(2)).

Example

0.63209866105082925035545064599078...

Mathematica

RealDigits[SequenceLimit[1`200 Table[(2 - Power @@ Table[Sqrt[2], {n}])/Log[2]^n, {n, 1, 200}]], 10, 100][[1]]

Crossrefs

Cf. A198094, A260691.

Sequence in context: A108451 A122178 A126445 * A033326 A068996 A362871

Adjacent sequences: A277432 A277433 A277434 * A277436 A277437 A277438

Keyword

nonn,cons

Author

Vladimir Reshetnikov, Oct 14 2016

Status

approved