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

0, 1, 4, 65536, 7625597484987

Offset: 1

Author

Natan Arie Consigli, May 07 2015

Keywords

• nonn
• bref

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A001597, A257309.