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 A214369 #41 Jan 30 2022 15:57:20
%S A214369 6,8,2,1,5,3,5,0,2,6,0,5,2,3,8,0,6,6,7,6,1,2,6,3,1,8,6,2,2,6,6,2,4,0,
%T A214369 0,9,6,4,9,1,9,0,2,4,8,3,2,6,9,0,3,4,1,9,2,2,8,2,5,7,8,4,7,1,3,6,7,7,
%U A214369 1,8,3,4,7,7,4,1,7,8,7,3,2,9,0,0,9,6,2,1,2,6,9,0,3,0,4,5,3,3,1,3,7,5,0,3,2
%N A214369 Decimal expansion of Sum_{n>=1} 1/(3^n-1).
%H A214369 G. C. Greubel, <a href="/A214369/b214369.txt">Table of n, a(n) for n = 0..10000</a>
%F A214369 Equals Sum_{n>=1} 1/A024023(n).
%F A214369 Equals Sum_{k>=1} d(k)/3^k, where d(k) is the number of divisors of k (A000005). - _Amiram Eldar_, May 17 2020
%e A214369 Equals 0.6821535026052380667...
%p A214369 evalf(sum(1/(3^k-1), k=1..infinity), 120); # _Vaclav Kotesovec_, Oct 18 2014
%p A214369 # second program with faster converging series
%p A214369 evalf( add( (1/3)^(n^2)*(1 + 2/(3^n - 1)), n = 1..14 ), 105); # _Peter Bala_, Jan 30 2022
%t A214369 RealDigits[ NSum[1/(3^n - 1), {n, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 100], 10, 105] // First (* or *) 1 - (Log[2] + QPolyGamma[0, 1, 1/3])/Log[3] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Jun 05 2013 *)
%t A214369 x = 1/3; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* _Robert G. Wilson v_, Oct 12 2014 after an observation and the formula of _Amarnath Murthy_, see A073668 *)
%o A214369 (PARI) suminf(n=1, 1/(3^n-1)) \\ _Michel Marcus_, Mar 11 2017
%Y A214369 Cf. A024023, A065442, A073668, A248721, A248722, A248723, A248724, A248725, A248726.
%K A214369 cons,nonn
%O A214369 0,1
%A A214369 _R. J. Mathar_, Jul 14 2012
%E A214369 More terms from _Jean-François Alcover_, Feb 12 2013