A133376 a(n) = (...((2^3)^4)^...)^n.

2, 8, 4096, 1152921504606846976, 2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976

Offset: 2

Author

Pierre Karpman (pierre.karpman(AT)laposte.net), Oct 28 2007

Keywords

• nonn

Comments

Another kind of exponential factorial.

See cross-references for other possible definitions of exponential factorials.

Some other terms of the sequence can be computed, but they are quite large and it wouldn't be very convenient to display them.

The next term has 759 digits. - Harvey P. Dale, Oct 22 2019

Examples

			a(4) = 4096, as (2^3)^4 = 4096.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..7

Crossrefs

Cf. A124075, A049384.

Programs

Maple

expfact:= proc(n::integer) local i,res; res:=2; for i from 3 to n do res:=(res)^i od; res end proc; seq(expfact(n), n=2..7);
# second Maple program:
a:= proc(n) option remember;
      `if`(n<3, n, a(n-1)^n)
    end:
seq(a(n), n=2..6);  # Alois P. Heinz, Jan 17 2024

Mathematica

nxt[{n_,a_}]:={n+1,a^(n+1)}; NestList[nxt,{2,2},4][[All,2]] (* Harvey P. Dale, Oct 22 2019 *)

Formula

a(n) = 2^(n!/2) for n >= 2. - Karl W. Heuer, Nov 25 2014