A383817 Decimal expansion of -Sum_{k>=1} mu(3*k)/(3^k - 1), where mu is the Möbius function A008683.

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

Offset

0,1

Comments

The real root of the cubic polynomial 729*x^3 - 810*x^2 - 429*x + 233 matches this constant to 20 decimal places.

Links

Table of n, a(n) for n=0..86.

Maxie Dion Schmidt, A catalog of interesting and useful Lambert series identities, arXiv:2004.02976 [math.NT], 2004(2020), page 9, eq. (3.1h), put q = 1/3 and alpha = 3. - Amiram Eldar, May 11 2025

Formula

Equals Sum_{k>=0} 1/3^(3^k) = Sum_{k>=0} 1/A055777(k). - Amiram Eldar, May 11 2025

Example

0.3704211756339267984957431894112681...

Prog

(PARI) sum(k=1, logint(2^getlocalbitprec(), 3)+1, moebius(3*k)/(3.^k - 1), 0.) \\ Bill Allombert

Crossrefs

Cf. A007404, A055777, A383818, A383819, A383820.

Sequence in context: A180873 A021031 A396212 * A291835 A197835 A197005

Adjacent sequences: A383814 A383815 A383816 * A383818 A383819 A383820

Keyword

nonn,cons

Author

Artur Jasinski, May 11 2025

Status

approved