cp's OEIS Frontend

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

%I A383817 #31 May 16 2025 17:35:19
%S A383817 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,
%T A383817 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,
%U A383817 3,8,6,7,8,3,1,5,7,3,5,1,5,6,5,6,0,1,0
%N A383817 Decimal expansion of -Sum_{k>=1} mu(3*k)/(3^k - 1), where mu is the Möbius function A008683.
%C A383817 The real root of the cubic polynomial 729*x^3 - 810*x^2 - 429*x + 233 matches this constant to 20 decimal places.
%H A383817 Maxie Dion Schmidt, <a href="https://arxiv.org/abs/2004.02976">A catalog of interesting and useful Lambert series identities</a>, arXiv:2004.02976 [math.NT], 2004(2020), page 9, eq. (3.1h), put q = 1/3 and alpha = 3. - _Amiram Eldar_, May 11 2025
%F A383817 Equals Sum_{k>=0} 1/3^(3^k) = Sum_{k>=0} 1/A055777(k). - _Amiram Eldar_, May 11 2025
%e A383817 0.3704211756339267984957431894112681...
%o A383817 (PARI) sum(k=1,logint(2^getlocalbitprec(),3)+1,moebius(3*k)/(3.^k - 1),0.) \\ Bill Allombert
%Y A383817 Cf. A007404, A055777, A383818, A383819, A383820.
%K A383817 nonn,cons
%O A383817 0,1
%A A383817 _Artur Jasinski_, May 11 2025