This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A277522 #29 Feb 16 2025 08:33:37 %S A277522 5,6,9,2,4,5,2,0,4,4,2,6,3,4,8,0,6,1,0,6,5,3,3,0,4,7,7,8,4,1,9,6,6,9, %T A277522 0,5,2,6,3,8,6,5,9,7,3,1,4,6,3,0,2,7,6,4,5,4,9,8,0,1,1,6,7,9,1,8,3,1, %U A277522 1,5,4,2,1,1,3,4,6,7,0,8,7,6,2,3,2,4,0,6,7,4,8,7,9,2,6,3,5,0,2,4,5,1,5,0,3 %N A277522 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/2. %H A277522 Alois P. Heinz, <a href="/A277522/b277522.txt">Table of n, a(n) for n = 0..1000</a> %H A277522 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a>. %H A277522 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>. %F A277522 Equals 2*exp(-2*LambertW(log(2)))/(1+LambertW(log(2))). - _Vladimir Reshetnikov_, Oct 20 2016 %e A277522 0.5692452044263480610653304778419669052638659731463... %t A277522 RealDigits[2 Exp[-2 ProductLog[Log[2]]]/(1 + ProductLog[Log[2]]), 10, 105][[1]] (* _Vladimir Reshetnikov_, Oct 20 2016 *) %t A277522 f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'[1/2], 10, 120][[1]] (* _Amiram Eldar_, May 23 2023 *) %o A277522 (PARI) 2*exp(-2*lambertw(log(2)))/(1+lambertw(log(2))) \\ _G. C. Greubel_, Nov 10 2017 %Y A277522 Cf. A033917, A104748, A277523, A277524, A277525, A277526, A277527, A277528, A277529, A277530, A277531, A277559, A277651, A293009, A300916. %K A277522 nonn,cons %O A277522 0,1 %A A277522 _Alois P. Heinz_, Oct 19 2016