A375378 Value of the power tower formed by the numbers in the n-th composition (in standard order).

1, 1, 2, 1, 3, 2, 1, 1, 4, 3, 4, 2, 1, 1, 1, 1, 5, 4, 9, 3, 8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 16, 4, 27, 9, 3, 3, 16, 8, 16, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 6, 25, 5, 64, 16, 4, 4, 81, 27, 81, 9, 3, 3, 3, 3, 32, 16

Offset: 0

Author

Pontus von Brömssen, Aug 14 2024

Keywords

• nonn

Comments

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

Examples

			For n = 38, the 38th composition is (3,1,2), so a(38) = 3^1^2 = 3^1 = 3.
		

Crossrefs

Cf. A004760, A053645, A065120, A066099 (compositions in standard order), A375379.

Formula

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

a(n) = 1 if and only if A065120(n) <= 1, i.e., if and only if n is in A004760.