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

Author

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

Keywords

• nonn
• cons
• fini

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.

Examples

			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].
		

Links

• Robert P. Munafo, Hyper4 Iterated Exponential Function..

Crossrefs

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

Programs

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)]

Formula

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

Extensions

Keyword: fini added by Jianing Song, Sep 18 2019