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

%I A277559 #26 Feb 16 2025 08:33:37
%S A277559 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 A277559 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 A277559 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 A277559 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = sqrt(2).
%C A277559 It is known that sqrt(2)^sqrt(2)^sqrt(2)^... = 2.
%H A277559 Alois P. Heinz, <a href="/A277559/b277559.txt">Table of n, a(n) for n = 1..1000</a>
%H A277559 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H A277559 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F A277559 Equals 2^(3/2)/(1-log(2)).
%F A277559 Equals A010466/A244009. - _Michel Marcus_, Oct 20 2016
%e A277559 9.21753670019231544705131363265247919608239799603795429...
%t A277559 RealDigits[Sqrt[8]/(1-Log[2]), 10, 100][[1]] (* _G. C. Greubel_, Jul 27 2018 *)
%o A277559 (PARI) sqrt(8)/(1-log(2)) \\ _Michel Marcus_, Oct 20 2016
%o A277559 (Magma) Sqrt(8)/(1-Log(2)); // _G. C. Greubel_, Jul 27 2018
%Y A277559 Cf. A002162, A002193, A010466, A244009, A277522, A277651.
%K A277559 nonn,cons
%O A277559 1,1
%A A277559 _Alois P. Heinz_, Oct 19 2016