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 A248726 #26 Jan 30 2022 15:58:04 %S A248726 1,3,9,0,4,5,1,1,7,6,6,2,1,8,8,1,2,9,3,5,8,7,2,8,4,7,4,3,6,9,0,8,9,0, %T A248726 5,2,1,3,9,3,6,2,6,4,7,0,6,7,8,1,9,6,0,9,5,5,1,0,3,5,4,9,3,4,7,9,6,7, %U A248726 0,2,0,1,4,5,3,6,6,6,6,0,7,9,8,8,6,3,3,7,9,8,1,3,5,7,6,5,5,0,5,7,9,9,5,5,3 %N A248726 Decimal expansion of Sum_{k>=1} 1/(9^k - 1). %H A248726 G. C. Greubel, <a href="/A248726/b248726.txt">Table of n, a(n) for n = 0..10000</a> %F A248726 Equals Sum_{k>=1} d(k)/9^k, where d(k) is the number of divisors of k (A000005). - _Amiram Eldar_, Jun 22 2020 %e A248726 0.13904511766218812935872847436908905213936264706781960955103549347967020145366... %p A248726 evalf(sum(1/(9^k-1), k=1..infinity),120) # _Vaclav Kotesovec_, Oct 18 2014 %p A248726 # second program with faster converging series %p A248726 evalf( add( (1/9)^(n^2)*(1 + 2/(9^n - 1)), n = 1..10), 105); # _Peter Bala_, Jan 30 2022 %t A248726 x = 1/9; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* after an observation and the formula of _Amarnath Murthy_, see A073668 *) %o A248726 (PARI) suminf(k=1, 1/(9^k-1)) \\ _Michel Marcus_, Oct 18 2014 %Y A248726 Cf. A000005, A065442, A073668, A214369, A248721, A248722, A248723, A248724, A248725. %K A248726 nonn,cons %O A248726 0,2 %A A248726 _Robert G. Wilson v_, Oct 12 2014