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A383819 Decimal expansion of -Sum_{k>=1} mu(3*k)/(27^k + 1), where mu is the Möbius function.

%I A383819 #13 May 21 2025 00:59:53
%S A383819 0,3,4,3,4,4,3,5,2,9,1,3,2,7,8,1,7,5,2,8,8,8,2,7,5,2,9,0,3,4,4,9,6,9,
%T A383819 3,1,4,1,9,9,4,4,2,0,3,2,9,7,5,2,1,0,4,9,5,4,4,8,0,3,9,8,6,3,4,3,9,1,
%U A383819 5,3,9,1,9,4,8,1,0,2,0,7,3,3,9,5,4,4,6,3,0,0,2,7,4,5,6,4,8,7,7,4,3,0,1,7,5,0,4,4,1,8,2
%N A383819 Decimal expansion of -Sum_{k>=1} mu(3*k)/(27^k + 1), where mu is the Möbius function.
%F A383819 Equals Sum_{k>=1} (1/3^(3^k) - 2/3^(2*3^k)). - _Amiram Eldar_, May 16 2025
%e A383819 0.034344352913278175288827529...
%t A383819 Join[{0}, RealDigits[NSum[1/3^(3^k) - 2/3^(2*3^k), {k, 1, Infinity}, WorkingPrecision -> 120]][[1]]] (* _Amiram Eldar_, May 16 2025 *)
%o A383819 (PARI) -sum(k=1,logint(2^getlocalbitprec(),3)+1,moebius(3*k)/(27.^k + 1),0.) \\ Bill Allombert
%Y A383819 Cf. A008683, A383817, A383820.
%K A383819 nonn,cons
%O A383819 0,2
%A A383819 _Artur Jasinski_, May 16 2025