A218583 Decimal expansion of the limit of the n-fold application of the natural logarithm to A049384 as n tends to infinity.

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, 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, 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

Offset: 0

Author

Benedikt Otten, Nov 03 2012

Keywords

• nonn
• cons

Comments

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

Examples

			-0.0613312423000835123439855996950060450612102645287...
		

Links

• Proof that the series converges (StackExchange, 10/09/2012)

Crossrefs

Cf. A049384.

Programs

Mathematica

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]

Formula

Equals -log(...log(n^(n-1)^...^1)...) (n nested log).