|
%I #16 Sep 18 2019 14:05:30
%S 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,
%T 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,
%U 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
%N Decimal expansion of 5^(5^(5^5)) = 5^^4.
%C 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.
%H Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html"> Hyper4 Iterated Exponential Function.</a>.
%F 5^(5^(5^5)) = ((((( ... 3114 ... (((((5^5)^5)^5)^5)^5) ... 3114 ... ^5)^5)^5)^5)^5)^5.
%e 1111028808179997445286178274186057545167346520596272154733386745225196554833740184735209940181105736...(1.335740484... * 10^2184)...3293393812245587348839009777160541868907233602002347435809721798438687301313620992004871368408203125.
%e The above line shows the first one hundred decimal digits and the last one hundred digits with the number of unrepresented digits in parenthesis.
%e The final one hundred digits where computed by: PowerMod[5, 5^5^5, 10^100].
%t 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 *)
%t 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)]
%Y Cf. A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241295, A241296, A241297, A241298, A241299, A243913.
%K nonn,cons,fini
%O 1,6
%A _Robert Munafo_ and _Robert G. Wilson v_, Apr 18 2014
%E Keyword: fini added by _Jianing Song_, Sep 18 2019
|
