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

2, 8, 4096, 1152921504606846976, 2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976

Offset

2,1

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A124075, A049384.

Sequence in context: A174736 A324567 A135238 * A179056 A160814 A038582

Adjacent sequences: A133373 A133374 A133375 * A133377 A133378 A133379

Keyword

nonn

Author

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

Status

approved