A353005 Decimal expansion of the root of the equation Sum_{k>0} x^k/(1-x^k) = 1.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Sylvie Corteel and Paweł Hitczenko, Generalizations of Carlitz Compositions, Journal of Integer Sequences, Vol. 10 (2007), Article 07.8.8., p. 7.

Formula

Root of the equation Sum_{k>0} A000005(k)*x^k = 1.

Equals lim_{n->infinity} 1/A129921(n)^(1/n).

Example

0.40614800500124722886895860305904194556294019393687243206705449364766416677475...

Mathematica

RealDigits[x/.FindRoot[QPolyGamma[0, 1, x]==Log[x/(1-x)], {x, 1/2}, WorkingPrecision->110]][[1]]

Crossrefs

Cf. A129921.

Sequence in context: A195207 A157721 A085968 * A010637 A200692 A360044

Adjacent sequences: A353002 A353003 A353004 * A353006 A353007 A353008

Keyword

nonn,cons

Author

Vaclav Kotesovec, Apr 15 2022

Status

approved