A241294 Decimal expansion of 5^(5^(5^5)) = 5^^4.

1, 1, 1, 1, 0, 2, 8, 8, 0, 8, 1, 7, 9, 9, 9, 7, 4, 4, 5, 2, 8, 6, 1, 7, 8, 2, 7, 4, 1, 8, 6, 0, 5, 7, 5, 4, 5, 1, 6, 7, 3, 4, 6, 5, 2, 0, 5, 9, 6, 2, 7, 2, 1, 5, 4, 7, 3, 3, 3, 8, 6, 7, 4, 5, 2, 2, 5, 1, 9, 6, 5, 5, 4, 8, 3, 3, 7, 4, 0, 1, 8, 4, 7, 3, 5, 2, 0, 9, 9, 4, 0, 1, 8, 1, 1, 0, 5, 7, 3, 6, 4, 3, 5, 0, 9

Offset

1,6

Comments

The offset is 1 because the true offset would be 1.335740484... * 10^2184, which is too large to be represented properly in the OEIS.

Links

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

Robert P. Munafo, Hyper4 Iterated Exponential Function..

Formula

5^(5^(5^5)) = ((((( ... 3114 ... (((((5^5)^5)^5)^5)^5) ... 3114 ... ^5)^5)^5)^5)^5)^5.

Example

1111028808179997445286178274186057545167346520596272154733386745225196554833740184735209940181105736...(1.335740484... * 10^2184)...3293393812245587348839009777160541868907233602002347435809721798438687301313620992004871368408203125.
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[5, 5^5^5, 10^100].

Mathematica

nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 5, 5^5^5] (* or *)
p = 5; f[n_] := Quotient[n^p, 10^(Floor[p * Log10@ n] - (1004 + p^p))]; IntegerDigits@ Quotient[ Nest[ f@ # &, p, p^p], 10^(900 + p^p)]

Crossrefs

Cf. A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241295, A241296, A241297, A241298, A241299, A243913.

Sequence in context: A344692 A256166 A021976 * A196775 A021351 A011061

Adjacent sequences: A241291 A241292 A241293 * A241295 A241296 A241297

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