A277524 Decimal expansion of the third derivative of the infinite power tower function x^x^x... at x = 1/2.

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

Author

Alois P. Heinz, Oct 19 2016

Keywords

• nonn
• cons

Examples

			1.901713907526003986262639982124699514446488574524050...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Power Tower.
• Wikipedia, Tetration.

Crossrefs

Cf. A033917, A104748, A277522, A277523, A277525, A277526, A277527, A277528, A277529, A277530, A277531.

Programs

Mathematica

f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'''[1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)