cp's OEIS Frontend

A073233 Decimal expansion of Pi^Pi.

%I A073233 #32 Aug 20 2024 23:18:48
%S A073233 3,6,4,6,2,1,5,9,6,0,7,2,0,7,9,1,1,7,7,0,9,9,0,8,2,6,0,2,2,6,9,2,1,2,
%T A073233 3,6,6,6,3,6,5,5,0,8,4,0,2,2,2,8,8,1,8,7,3,8,7,0,9,3,3,5,9,2,2,9,3,4,
%U A073233 0,7,4,3,6,8,8,8,1,6,9,9,9,0,4,6,2,0,0,7,9,8,7,5,7,0,6,7,7,4,8,5,4,3,6,8,1
%N A073233 Decimal expansion of Pi^Pi.
%C A073233 A weak form of Schanuel's Conjecture implies that Pi^Pi is transcendental--see Marques and Sondow (2012).
%H A073233 Harry J. Smith, <a href="/A073233/b073233.txt">Table of n, a(n) for n = 2..20000</a>
%H A073233 D. Marques and J. Sondow, <a href="http://arxiv.org/abs/1212.6931">The Schanuel Subset Conjecture implies Gelfond's Power Tower Conjecture</a>, arXiv:1212.6931 [math.NT], 2012-2013.
%e A073233 36.4621596072079117709908260226...
%t A073233 RealDigits[N[Pi^Pi,200]] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2010 *)
%o A073233 (PARI) Pi^Pi
%o A073233 (PARI) { default(realprecision, 20080); x=Pi^Pi/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b073233.txt", n, " ", d)); } \\ _Harry J. Smith_, Apr 30 2009
%Y A073233 Cf. A000796 (Pi), A073234 (Pi^Pi^Pi), A073237 (ceil(Pi^Pi^...^Pi), n Pi's), A073238 (Pi^(1/Pi)), A073239 ((1/Pi)^Pi), A073240 ((1/Pi)^(1/Pi)), A073243 (limit of (1/Pi)^(1/Pi)^...^(1/Pi)), A073236 (Pi analog of A004002).
%Y A073233 Cf. A073226 (e^e).
%Y A073233 Cf. A049006 (i^i), A116186 (real part of i^i^i).
%Y A073233 Cf. A194555 (real part of i^e^Pi).
%K A073233 cons,nonn
%O A073233 2,1
%A A073233 _Rick L. Shepherd_, Jul 21 2002