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

0,2

Comments

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

Links

Table of n, a(n) for n=0..98.

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

Formula

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

Example

-0.0613312423000835123439855996950060450612102645287...

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]

Crossrefs

Cf. A049384.

Sequence in context: A074453 A069608 A211453 * A181166 A273191 A086316

Adjacent sequences: A218580 A218581 A218582 * A218584 A218585 A218586

Keyword

nonn,cons

Author

Benedikt Otten, Nov 03 2012

Status

approved