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

Author

Pontus von Brömssen, Aug 14 2024

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Formula

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