A277651 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/4.

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

Author

Alois P. Heinz, Oct 25 2016

Keywords

• nonn
• cons

Comments

It is known that (1/4)^(1/4)^(1/4)^... = 1/2.

Examples

			0.59061610914964124974380690932325155711665304887388...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Power Tower.
• Wikipedia, Tetration.

Crossrefs

Cf. A002162, A277522, A277559, A293009, A300916.

Programs

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 *)

Formula

Equals 1/(1 + log(2)) = 1/(1 + A002162).

Equals Integral_{x >= 0} exp(-x)/2^x dx. - Peter Bala, Feb 05 2024