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A277524
Decimal expansion of the third derivative of the infinite power tower function x^x^x... at x = 1/2.
10
1, 9, 0, 1, 7, 1, 3, 9, 0, 7, 5, 2, 6, 0, 0, 3, 9, 8, 6, 2, 6, 2, 6, 3, 9, 9, 8, 2, 1, 2, 4, 6, 9, 9, 5, 1, 4, 4, 4, 6, 4, 8, 8, 5, 7, 4, 5, 2, 4, 0, 5, 0, 5, 3, 1, 6, 2, 0, 0, 0, 9, 0, 0, 9, 1, 3, 5, 1, 5, 9, 4, 3, 5, 4, 5, 0, 7, 5, 5, 4, 2, 9, 0, 3, 4, 9, 2, 6, 8, 4, 0, 1, 4, 2, 1, 2, 6, 0, 2, 6, 6, 8, 4, 7, 1, 6, 5
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Power Tower.
Wikipedia, Tetration.
EXAMPLE
1.901713907526003986262639982124699514446488574524050...
MATHEMATICA
f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'''[1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, Oct 19 2016
STATUS
approved