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

1, 3, 36, 1340164183006357435

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

Links

Table of n, a(n) for n=0..3.

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

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

Sequence in context: A006268 A264842 A210508 * A372478 A002563 A140448

Adjacent sequences: A073233 A073234 A073235 * A073237 A073238 A073239

Keyword

nonn

Author

Rick L. Shepherd, Jul 25 2002

Status

approved