A277559 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = sqrt(2).

9, 2, 1, 7, 5, 3, 6, 7, 0, 0, 1, 9, 2, 3, 1, 5, 4, 4, 7, 0, 5, 1, 3, 1, 3, 6, 3, 2, 6, 5, 2, 4, 7, 9, 1, 9, 6, 0, 8, 2, 3, 9, 7, 9, 9, 6, 0, 3, 7, 9, 5, 4, 2, 9, 0, 3, 1, 1, 2, 0, 8, 4, 1, 2, 7, 3, 3, 3, 2, 2, 5, 3, 6, 7, 3, 5, 0, 3, 0, 2, 9, 0, 7, 5, 7, 4, 5, 7, 5, 1, 5, 2, 2, 5, 4, 3, 0, 7, 9, 3, 2, 4, 2, 0, 2

Offset: 1

Author

Alois P. Heinz, Oct 19 2016

Keywords

• nonn
• cons

Comments

It is known that sqrt(2)^sqrt(2)^sqrt(2)^... = 2.

Examples

			9.21753670019231544705131363265247919608239799603795429...
		

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. A002162, A002193, A010466, A244009, A277522, A277651.

Programs

Magma

Sqrt(8)/(1-Log(2)); // G. C. Greubel, Jul 27 2018

Mathematica

RealDigits[Sqrt[8]/(1-Log[2]), 10, 100][[1]] (* G. C. Greubel, Jul 27 2018 *)

PARI

sqrt(8)/(1-log(2)) \\ Michel Marcus, Oct 20 2016

Formula

Equals 2^(3/2)/(1-log(2)).

Equals A010466/A244009. - Michel Marcus, Oct 20 2016