A202955 - OEIS

%I #21 Dec 05 2019 20:54:05

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

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

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

%N Decimal expansion of Pi^Pi^Pi^Pi.

%C The offset equals the floor(Pi^Pi^Pi*Log_10(Pi))+1. - _Robert G. Wilson v_, Mar 13 2014

%C Whether this number is an integer or not is an open question. It is also an open question whether Pi^Pi^Pi^...^Pi^Pi n times is an integer for any natural n > 4. - _Eliora Ben-Gurion_, Nov 17 2019

%F A000796^A073234.

%e 9.080222455390617769723931713284287746516046358131897359946935926336845199... *10^666262452970848503

%t nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[exp*Log10[base], nbrdgt + Floor[Log10[exp]] + 2]], 10, nbrdgt][[1]]; f[Pi, Pi^Pi^Pi] (* _Robert G. Wilson v_, Mar 13 2014 *)

%o (PARI) LP(a,b)=[10^frac(a=log(a)/log(10)*b),a\1] /* returns [m,e] such that a^b = m*10^e */

%o LP(Pi,Pi^Pi^Pi)

%Y Cf. A073236, A085667, A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073235 ((Pi^Pi)^Pi), A202953 ((Pi^Pi)^(Pi^Pi)).

%K nonn,cons

%O 666262452970848504,1

%A _M. F. Hasler_, Dec 26 2011