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

Author

Artur Jasinski, May 11 2025

Keywords

• nonn
• cons

Comments

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

Examples

			0.3704211756339267984957431894112681...
		

Links

• 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

Crossrefs

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

Programs

PARI

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

Formula

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