A073236 - OEIS

%I #25 Jul 20 2024 19:48:05

%S 1,3,36,1340164183006357435

%N Pi^Pi^...^Pi (n times) rounded to nearest integer.

%C Decimal expansions (before rounding) of Pi (A000796), Pi^Pi (A073233) and Pi^Pi^Pi (A073234) correspond to a(1), a(2) and a(3), respectively. All four terms are equivalent if floor is used instead of round. See A073237 for same sequence but using ceiling. This sequence is the analog of A004002, which deals with e.

%C a(4) has 666262452970848504 digits. - _Mateusz Winiarski_, Mar 23 2020; corrected by _Martin Renner_, Aug 23 2023

%F a(n) = round(Pi^Pi^...^Pi), where Pi occurs n times, a(0) = 1 (=Pi^0).

%p p:= n-> `if`(n=0, 1, Pi^p(n-1)):

%p a:= n-> round(p(n)):

%p seq(a(n), n=0..3);  # _Alois P. Heinz_, Jul 20 2024

%t Round[NestList[Power[Pi, #] &, 1, 3]] (* _Alonso del Arte_, Jul 02 2014 *)

%o (PARI) p=0; for(n=0,3, p=Pi^p; print1(round(p),",")) \\ n = 4 produces too large an exponent for PARI.

%Y Cf. A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073237 (Ceiling of Pi^Pi^...^Pi, n times), A004002 (Benford numbers).

%K nonn

%O 0,2

%A _Rick L. Shepherd_, Jul 25 2002