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%I #5 Aug 17 2024 13:57:56
%S 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,
%T 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,
%U 25,5,64,16,4,4,81,27,81,9,3,3,3,3,32,16
%N Value of the power tower formed by the numbers in the n-th composition (in standard order).
%C It is natural to define a(0) = 1.
%F a(n) = A065120(n)^a(A053645(n)) for n >= 1.
%F a(n) = 1 if and only if A065120(n) <= 1, i.e., if and only if n is in A004760.
%e For n = 38, the 38th composition is (3,1,2), so a(38) = 3^1^2 = 3^1 = 3.
%Y Cf. A004760, A053645, A065120, A066099 (compositions in standard order), A375379.
%K nonn
%O 0,3
%A _Pontus von Brömssen_, Aug 14 2024