A073236 Pi^Pi^...^Pi (n times) rounded to nearest integer.

1, 3, 36, 1340164183006357435

Offset: 0

Author

Rick L. Shepherd, Jul 25 2002

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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