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 A257769 Perfect hyper-5 powers: a^^^b, where b <> 1. 1

%I

%S 0,1,4,65536,7625597484987

%N Perfect hyper-5 powers: a^^^b, where b <> 1.

%C a^^b (a to the hyper-4 power b) is the right associative power tower a^a^...^a^a of height b.

%C a^^^b (a to the hyper-5 power b) is the right associative hyper-4 power tower a^^a^^...^^a^^a of height b. a^^^-1 = 0, a^^^0 = 1;

%C We exclude b=1 because otherwise all natural numbers would be in the sequence.

%e Numbers satisfying the properties stated above:

%e 3^^^2 = 3^^3 = 3^3^3 = 3^27 = 7625597484987;

%e 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536;

%e 1^^^4 = 1^^1^^1^^1 = 1.

%Y Cf. A001597, A257309.

%K nonn,bref

%O 1,3

%A _Natan Arie Consigli_, May 07 2015

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Last modified December 5 13:58 EST 2022. Contains 358588 sequences. (Running on oeis4.)