A241296 - OEIS

%I #19 Sep 20 2019 12:29:39

%S 7,8,3,3,0,0,5,2,3,7,4,8,0,0,5,5,5,6,5,4,0,3,8,5,4,0,9,4,7,5,4,6,5,3,

%T 0,8,2,9,1,9,0,4,4,3,9,8,5,5,8,7,7,0,1,3,1,4,8,2,1,1,9,7,0,3,1,8,5,0,

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

%N Decimal expansion of 7^(7^(7^7)) = 7^^4.

%C The offset is 1 because the true offset would be 3.177419493... * 10^695974, 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 7^(7^(7^7)) = ((((( ... 823532 ... (((((7^7)^7)^7)^7)^7) ... 823532 ... ^7)^7)^7)^7)^7)^7.

%e 7833005237480055565403854094754653082919044398558770131482119703185028436339726344442972338289410045...(3.177419493... * 10^695974)...1766659134033863120639301828875443004447501140571853058472378511366058254036038182879357182733172343.

%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[7, 7^7^7, 10^100].

%t nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 7, 7^7^7]

%Y Cf. A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, A241295, A241297, A241298, A241299, A243913.

%K nonn,cons,fini

%O 1,1

%A _Robert Munafo_ and _Robert G. Wilson v_, Apr 18 2014

%E Keyword: fini added by _Jianing Song_, Sep 18 2019