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A241293
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Decimal expansion of 4^(4^(4^4)) = 4^^4.
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13
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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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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.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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