A306579 Decimal expansion of the real number x such that f(x) = x^x^x^x is a minimum.
2, 7, 4, 6, 8, 9, 3, 8, 5, 2, 9, 7, 0, 6, 3, 4, 6, 2, 4, 1, 3, 6, 2, 5, 3, 0, 0, 5, 3, 8, 1, 4, 5, 8, 5, 7, 5, 7, 8, 9, 9, 8, 8, 6, 5, 4, 3, 1, 2, 7, 7, 7, 0, 5, 4, 1, 2, 8, 1, 8, 6, 3, 6, 2, 8, 0, 3, 1, 6, 0, 4, 5, 0, 4, 0, 7, 2, 8, 3, 8, 8, 9, 3, 2, 6, 8, 3, 1, 1, 5, 5, 8, 4, 6, 6, 8, 0, 6, 0, 9, 5, 8, 2, 0, 4, 5, 7, 4, 0, 6
Offset: 0
Examples
0.274689385297063462413625300538145857578998865431277705412818636280...
Programs
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Mathematica
n = 500; (x /. FindMinimum[x^x^x^x, {x, 0.34}, WorkingPrecision -> 3 n][[2]][[1]] // RealDigits)[[1]][[;; n]] -
PARI
solve(x=0.1, 1, 1 + x^x*log(x)*(1 + x*log(x)*(1 + log(x)))) \\ Michel Marcus, Mar 15 2019
Comments