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A218583
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Decimal expansion of the limit of the n-fold application of the natural logarithm to A049384 as n tends to infinity.
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0
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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
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OFFSET
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0,2
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COMMENTS
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The value can be calculated to an accuracy of at least 4.8×10^183230 decimal digits by calculating log(...log(7^...^1)...).
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LINKS
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FORMULA
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-log(...log(n^(n-1)^...^1)...)(n nested log)
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EXAMPLE
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-0.0613312423000835123439855996950060450612102645287...
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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