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A241293
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Decimal expansion of 4^(4^(4^4)) = 4^^4.
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11
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2, 3, 6, 1, 0, 2, 2, 6, 7, 1, 4, 5, 9, 7, 3, 1, 3, 2, 0, 6, 8, 7, 7, 0, 2, 7, 4, 9, 7, 7, 8, 1, 7, 9, 4, 3, 0, 9, 4, 6, 1, 2, 7, 2, 9, 1, 4, 7, 7, 5, 1, 5, 4, 4, 6, 7, 1, 9, 2, 5, 6, 9, 4, 6, 2, 1, 2, 7, 1, 1, 8, 5, 3, 6, 6, 6, 4, 7, 5, 5, 2, 4, 9, 4, 5, 7, 6, 9, 3, 5, 0, 1, 0, 1, 9, 4, 1, 9, 9, 7, 7, 1, 6, 1, 6
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OFFSET
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1,1
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COMMENTS
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The offset is 1 because the true offset would be 8.072304726...*10^153, which is too large to be represented properly in the OEIS.
This is the decimal expansion of 2^2^513. - Jianing Song, Dec 25 2018
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LINKS
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Table of n, a(n) for n=1..105.
Robert P. Munafo, Hyper4 Iterated Exponential Function..
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FORMULA
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4^(4^(4^4)) = ((((( ... 245 ... (((((4^4)^4)^4)^4)^4) ... 245 ... ^4)^4)^4)^4)^4)^4.
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EXAMPLE
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2361022671459731320687702749778179430946127291477515446719256946212711853666475524945769350101941997...(8.072304726...*10^153)...7470426497333490366540651560537534642789067586985427238232605843019607448189676936860456095261392896.
The above line shows the first one hundred decimal digits and the last one hundred digits with the number of unrepresented digits in parenthesis.
The final one hundred digits where computed by: PowerMod[4, 4^4^4, 10^100].
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MATHEMATICA
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nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 4, 4^4^4] (* or *)
p = 4; f[n_] := Quotient[n^p, 10^(Floor[p * Log10@ n] - (1004 + p^p))]; IntegerDigits@ Quotient[ Nest[ f@ # &, p, p^p], 10^(900 + p^p)] (* Program fixed by Jianing Song, Sep 18 2019 *)
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CROSSREFS
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Cf. A114561, A085667, A202955, A054382, A014221, A241291, A241292, A241294, A241295, A241296, A241297, A241298, A241299, A243913.
Sequence in context: A082052 A232930 A217100 * A107409 A268603 A226871
Adjacent sequences: A241290 A241291 A241292 * A241294 A241295 A241296
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KEYWORD
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nonn,cons,fini
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AUTHOR
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Robert Munafo and Robert G. Wilson v, Apr 18 2014
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EXTENSIONS
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Keyword: fini added by Jianing Song, Sep 18 2019
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STATUS
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approved
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