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

1,2

Comments

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

Links

Table of n, a(n) for n=1..100.

Example

1.604651218410055827983866511015173398808649754699580...

Prog

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

Crossrefs

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

Sequence in context: A341325 A021947 A073010 * A132709 A197148 A196623

Adjacent sequences: A100117 A100118 A100119 * A100121 A100122 A100123

Keyword

cons,nonn

Author

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

Extensions

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

Status

approved