A277559 - OEIS

%I #25 Dec 18 2024 17:39:20

%S 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,

%T 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,

%U 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

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

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

%H Alois P. Heinz, <a href="/A277559/b277559.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>

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

%F Equals A010466/A244009. - _Michel Marcus_, Oct 20 2016

%e 9.21753670019231544705131363265247919608239799603795429...

%t RealDigits[Sqrt[8]/(1-Log[2]), 10, 100][[1]] (* _G. C. Greubel_, Jul 27 2018 *)

%o (PARI) sqrt(8)/(1-log(2)) \\ _Michel Marcus_, Oct 20 2016

%o (Magma) Sqrt(8)/(1-Log(2)); // _G. C. Greubel_, Jul 27 2018

%Y Cf. A002162, A002193, A010466, A244009, A277522, A277651.

%K nonn,cons

%O 1,1

%A _Alois P. Heinz_, Oct 19 2016