This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383820 #24 May 24 2025 00:14:16
%S A383820 0,3,7,0,8,7,8,4,2,3,0,0,5,9,3,4,6,5,1,6,2,4,0,9,8,5,6,0,7,7,9,3,4,7,
%T A383820 6,7,6,4,4,7,9,5,2,6,3,4,5,1,2,7,2,0,0,1,4,8,2,0,5,5,2,6,9,4,4,8,2,1,
%U A383820 0,5,3,4,4,9,8,2,4,0,1,8,2,3,2,2,6,7,7,2,3,9,2,4,3,1,0,0,7,9,4,9,4,8,2,3,8,5
%N A383820 Decimal expansion of Sum_{k>=1} 1/3^(3^k).
%C A383820 The real root of the cubic polynomial 243*x^3 - 27*x^2 - 242*x + 9 matches this constant to 20 decimal places.
%F A383820 Equals -Sum_{k>=1} mu(3*k)/(27*k-1), where mu is the Möbius function A008683.
%F A383820 Equals A383817 - 1/3.
%e A383820 0.037087842300593465162409856...
%t A383820 sum = Sum[1/3^(3^n), {n, 1, Infinity}]; nsum = N[sum, 110]; RealDigits[nsum, 10, 105][[1]]
%o A383820 (PARI) -sum(k=1,logint(2^getlocalbitprec(),3)+1,moebius(3*k)/(27.^k - 1),0.) \\ Bill Allombert
%o A383820 (PARI) suminf(k=1, 1/3^(3^k)) \\ _Amiram Eldar_, May 16 2025
%Y A383820 Cf. A008683, A383817, A383819.
%K A383820 nonn,cons
%O A383820 0,2
%A A383820 _Artur Jasinski_, May 16 2025