A100120 Limit of the power tower t(2)^(t(3)^(t(5)^(t(7)^(...)))) with t(n)=n!^(1/n!) and n taking prime values.

1, 6, 0, 4, 6, 5, 1, 2, 1, 8, 4, 1, 0, 0, 5, 5, 8, 2, 7, 9, 8, 3, 8, 6, 6, 5, 1, 1, 0, 1, 5, 1, 7, 3, 3, 9, 8, 8, 0, 8, 6, 4, 9, 7, 5, 4, 6, 9, 9, 5, 8, 0, 3, 4, 0, 4, 8, 4, 5, 7, 2, 7, 2, 8, 3, 2, 7, 1, 1, 4, 9, 2, 5, 5, 9, 9, 5, 4, 0, 0, 5, 3, 7, 9, 9, 1, 7, 5, 6, 0, 1, 9, 9, 0, 6, 5, 5, 9, 8, 2

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 09 2004

Keywords

• cons
• nonn

Comments

Let f(n)=n!^(1/n!). Then this number is f(2)^(f(3)^(f(5)^(...)))

Examples

			1.604651218410055827983866511015173398808649754699580...
		

Crossrefs

Cf. A077589, A077590, A073243, A098454, A098584.

Programs

PARI

default(realprecision,100):t=1:forstep(n=100,1,-1,t=(prime(n)!^(1/prime(n)!))^t):return(t)

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009