A218583 - OEIS

%I #17 Nov 02 2013 17:13:36

%S 0,6,1,3,3,1,2,4,2,3,0,0,0,8,3,5,1,2,3,4,3,9,8,5,5,9,9,6,9,5,0,0,6,0,

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

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

%N Decimal expansion of the limit of the n-fold application of the natural logarithm to A049384 as n tends to infinity.

%C The value can be calculated to an accuracy of at least 4.8×10^183230 decimal digits by calculating log(...log(7^...^1)...).

%H <a href="http://math.stackexchange.com/questions/216937/limit-of-log-log-logn-n-1">Proof that the series converges</a> (StackExchange, 10/09/2012)

%F -log(...log(n^(n-1)^...^1)...)(n nested log)

%e -0.0613312423000835123439855996950060450612102645287...

%t p[n_] := HoldForm[n]^(p[n - 1]); p[1] := 1; rules = {Log[x_ y_] :> Log[x] + Log[y], Log[x_^k_] :> k Log[x]}; lnn[x_, n_] := Log[lnn[x, n - 1]]; lnn[x_, 0] := x; RealDigits[ReleaseHold[lnn[p[7], 7] //. rules], 10, 100, 0]

%Y Cf. A049384.

%K nonn,cons

%O 0,2

%A _Benedikt Otten_, Nov 03 2012