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A277651
Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/4.
5
5, 9, 0, 6, 1, 6, 1, 0, 9, 1, 4, 9, 6, 4, 1, 2, 4, 9, 7, 4, 3, 8, 0, 6, 9, 0, 9, 3, 2, 3, 2, 5, 1, 5, 5, 7, 1, 1, 6, 6, 5, 3, 0, 4, 8, 8, 7, 3, 8, 8, 0, 0, 6, 7, 4, 4, 0, 2, 7, 9, 2, 0, 1, 9, 2, 1, 8, 2, 4, 9, 3, 3, 7, 5, 4, 4, 5, 7, 2, 7, 5, 2, 5, 4, 4, 3, 5, 2, 2, 3, 9, 4, 1, 8, 4, 8, 8, 3, 8, 6, 2, 6, 8, 9
OFFSET
0,1
COMMENTS
It is known that (1/4)^(1/4)^(1/4)^... = 1/2.
LINKS
Eric Weisstein's World of Mathematics, Power Tower.
Wikipedia, Tetration.
FORMULA
Equals 1/(1 + log(2)) = 1/(1 + A002162).
Equals Integral_{x >= 0} exp(-x)/2^x dx. - Peter Bala, Feb 05 2024
EXAMPLE
0.59061610914964124974380690932325155711665304887388...
MATHEMATICA
RealDigits[1/(1 + Log[2]), 10, 120][[1]]
(* or *)
f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'[1/4], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, Oct 25 2016
STATUS
approved