A202955 Decimal expansion of Pi^Pi^Pi^Pi.

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, 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, 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

Offset: 666262452970848504

Author

M. F. Hasler, Dec 26 2011

Keywords

• nonn
• cons

Comments

The offset equals the floor(Pi^Pi^Pi*Log_10(Pi))+1. - Robert G. Wilson v, Mar 13 2014

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

Examples

			9.080222455390617769723931713284287746516046358131897359946935926336845199... *10^666262452970848503
		

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Formula

A000796^A073234.