A073237 a(n) = ceiling(Pi^Pi^...^Pi), where Pi appears n times.

1, 4, 37, 1340164183006357436

Offset: 0

Author

Rick L. Shepherd, Jul 25 2002

Keywords

• nonn

Comments

Decimal expansions (before taking ceiling) of Pi (A000796), Pi^Pi (A073233) and Pi^Pi^Pi (A073234) correspond to a(1), a(2) and a(3), respectively. See A073236 for same sequence rounded to nearest integer. This sequence is similar to A004002, which deals with e (but rounds).

a(4) has 666262452970848504 digits. - Martin Renner, Aug 19 2023

Crossrefs

Cf. A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073236 (Pi^Pi^...^Pi, n times, rounded), A004002 (Benford numbers), A056072 (similar to A004002 but takes floor).

Programs

Maple

p:= n-> `if`(n=0, 1, Pi^p(n-1)):
a:= n-> ceil(p(n)):
seq(a(n), n=0..3);  # Alois P. Heinz, Jul 20 2024

PARI

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

Formula

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