A375379 Value of the power tower formed by the numbers obtained by adding 1 to the terms in the n-th composition (in standard order).

1, 2, 3, 4, 4, 9, 8, 16, 5, 16, 27, 81, 16, 512, 256, 65536, 6, 25, 64, 256, 81, 19683, 6561, 43046721, 32, 65536, 134217728, 2417851639229258349412352, 65536

Offset

0,2

Comments

This is a version of A375378 that does not allow 1's in the power towers.

It is natural to define a(0) = 1.

The number k >= 1 appears A294336(k) times as a term in this sequence.

Links

Pontus von Brömssen, Table of n, a(n) for n = 0..30

Formula

a(n) = (A065120(n)+1)^a(A053645(n)) for n >= 1.

Example

For n = 31, the 31st composition is (1, 1, 1, 1, 1), so a(31) = 2^2^2^2^2 = 2^65536.
For n = 37, the 37th composition is (3,2,1), so a(37) = 4^3^2 = 4^9 = 262144.

Crossrefs

Cf. A053645, A065120, A066099 (compositions in standard order), A294336, A375378.

Sequence in context: A228740 A269583 A250361 * A118263 A217478 A279788

Adjacent sequences: A375376 A375377 A375378 * A375380 A375381 A375382

Keyword

nonn

Author

Pontus von Brömssen, Aug 14 2024

Status

approved