OFFSET
0,2
COMMENTS
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.
a(4) has 666262452970848504 digits. - Mateusz Winiarski, Mar 23 2020; corrected by Martin Renner, Aug 23 2023
FORMULA
a(n) = round(Pi^Pi^...^Pi), where Pi occurs n times, a(0) = 1 (=Pi^0).
MAPLE
p:= n-> `if`(n=0, 1, Pi^p(n-1)):
a:= n-> round(p(n)):
seq(a(n), n=0..3); # Alois P. Heinz, Jul 20 2024
MATHEMATICA
Round[NestList[Power[Pi, #] &, 1, 3]] (* Alonso del Arte, Jul 02 2014 *)
PROG
(PARI) p=0; for(n=0, 3, p=Pi^p; print1(round(p), ", ")) \\ n = 4 produces too large an exponent for PARI.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jul 25 2002
STATUS
approved