A277522 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/2.

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, 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, 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

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Power Tower.

Wikipedia, Tetration.

Formula

Equals 2*exp(-2*LambertW(log(2)))/(1+LambertW(log(2))). - Vladimir Reshetnikov, Oct 20 2016

Example

0.5692452044263480610653304778419669052638659731463...

Mathematica

RealDigits[2 Exp[-2 ProductLog[Log[2]]]/(1 + ProductLog[Log[2]]), 10, 105][[1]] (* Vladimir Reshetnikov, Oct 20 2016 *)
f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[f'[1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)

Prog

(PARI) 2*exp(-2*lambertw(log(2)))/(1+lambertw(log(2))) \\ G. C. Greubel, Nov 10 2017

Crossrefs

Cf. A033917, A104748, A277523, A277524, A277525, A277526, A277527, A277528, A277529, A277530, A277531, A277559, A277651, A293009, A300916.

Sequence in context: A244274 A279664 A230461 * A019598 A340565 A197283

Adjacent sequences: A277519 A277520 A277521 * A277523 A277524 A277525

Keyword

nonn,cons

Author

Alois P. Heinz, Oct 19 2016

Status

approved