A293009 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/Pi.

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

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Tetration

Formula

Equals Pi*exp(-2*LambertW(log(Pi)))/(1+LambertW(log(Pi))).

Example

0.56501844596024150528994096062245192028392680078511838285519...

Mathematica

RealDigits[Pi*Exp[-2*LambertW[Log[Pi]]]/(1+LambertW[Log[Pi]]), 10, 100][[1]] (* G. C. Greubel, Sep 09 2018 *)

Prog

(PARI) Pi*exp(-2*lambertw(log(Pi)))/(1+lambertw(log(Pi))) \\ Michel Marcus, Mar 16 2018

Crossrefs

Cf. A000796, A049541, A073243, A277522, A277651, A300916.

Sequence in context: A144522 A371763 A020504 * A011004 A226975 A377635

Adjacent sequences: A293006 A293007 A293008 * A293010 A293011 A293012

Keyword

nonn,cons

Author

Alois P. Heinz, Mar 16 2018

Status

approved