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

Author

Philipp O. Tsvetkov, Mar 15 2019

Keywords

• nonn
• cons

Comments

It satisfies 1 + x^x*log(x)*(1 + x*log(x)*(1 + log(x))) = 0.

The function x^x has a minimum at x = 1/e (A068985).

Examples

			0.274689385297063462413625300538145857578998865431277705412818636280...
		

Crossrefs

Cf. A068985, A306883.

Programs

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