A364270 a(n) = 2^^n + 3^^n, where ^^ indicates tetration.

2, 5, 31, 7625597485003

Offset

0,1

Comments

a(4) has 3638334640025 digits and is too large to show here.

a(n) is prime for n = 0, 1, 2, 3, but it is not known if a(4) is prime.

From Zhining Yang, Feb 23 2026: (Start)

The least prime factor of a(4) is 21219553216129.

34276387 is a factor of a(k) for k >= 5.

4423 is a factor of a(k) for k >= 6.

42201151 is a factor of a(k) for k >= 7.

182668663 is a factor of a(k) for k >= 8. (End)

Links

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

Zhihu, Is 2^2^2^2+3^3^3^3 a prime number? (in Chinese).

Zhihu, Is 2^2^2^2+3^3^3^3 a prime number? (in Chinese).

Formula

a(n) = A014221(n) + A014222(n+1).

a(n) = A321312(2,n) + A321312(3,n).

Example

For n = 3, a(3) = 2^2^2 + 3^3^3 = 2^4 + 3^27 = 7625597485003.

Mathematica

nmax=3; NestList[2^#&, 1, nmax]+NestList[3^#&, 1, nmax] (* Stefano Spezia, Oct 22 2023 *)

Crossrefs

Cf. A004249, A014221, A014222, A321312.

Sequence in context: A259644 A132527 A182327 * A032504 A041397 A042811

Adjacent sequences: A364267 A364268 A364269 * A364271 A364272 A364273

Keyword

nonn,base,hard

Author

Marco Ripà, Oct 20 2023

Status

approved