A241293 Decimal expansion of 4^(4^(4^4)) = 4^^4.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..105.

Robert P. Munafo, Hyper4 Iterated Exponential Function..

Formula

4^(4^(4^4)) = ((((( ... 245 ... (((((4^4)^4)^4)^4)^4) ... 245 ... ^4)^4)^4)^4)^4)^4.

Example

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].

Mathematica

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 *)

Crossrefs

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

Keyword

nonn,cons,fini

Author

Robert Munafo and Robert G. Wilson v, Apr 18 2014

Extensions

Keyword: fini added by Jianing Song, Sep 18 2019

Status

approved