1,3

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

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;

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

Table of n, a(n) for n=1..5.

Numbers satisfying the properties stated above:

3^^^2 = 3^^3 = 3^3^3 = 3^27 = 7625597484987;

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

1^^^4 = 1^^1^^1^^1 = 1.

Cf. A001597, A257309.

Sequence in context: A074318 A276718 A102200 * A066544 A009529 A339450

Adjacent sequences: A257766 A257767 A257768 * A257770 A257771 A257772

nonn,bref

Natan Arie Consigli, May 07 2015

approved