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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.
3
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)^(...)))
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
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