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 A321873 #29 Feb 16 2025 08:33:57
%S A321873 1,2,6,3,2,9,3,0,5,8,1,0,0,2,7,1,3,3,1,8,8,7,9,7,2,6,6,3,9,0,3,1,3,9,
%T A321873 1,4,6,8,8,4,3,2,4,0,0,8,9,7,2,3,4,6,2,1,3,8,1,7,7,6,2,3,9,0,1,3,8,3,
%U A321873 1,4,1,1,1,4,6,6,2,1,9,4,0,8,2,5,5,7,1,1,0,5,4,2,7,5,9,5,2,3,8,6,1,7,8,5,3,7,3,3,3,1,6,3,7,0,2,9,6,7,6,3,0,8,9,2,7,1,9,6
%N A321873 Decimal expansion of the sum of reciprocals of repunit numbers base 4, Sum_{k>=1} 3/(4^k - 1).
%C A321873 The sums of reciprocal repunit numbers are related to the Lambert series. A special case is the sum of repunit numbers in base 2, which is known as the Erdős-Borwein constant (A065442).
%H A321873 N. Kurakowa and M. Wakyama, <a href="https://doi.org/10.1090/S0002-9939-03-07025-4">On q-analogues of the Euler Constant and Lerch's limit formula</a>, Proc. AMS 132 (4) (2003) 935, constant gamma(4).
%H A321873 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Erdos-BorweinConstant.html">Erdős-Borwein Constant</a>
%H A321873 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertSeries.html">Lambert Series</a>
%F A321873 Equals 3*L(1/4) = 3 * A248721, where L is the Lambert series.
%F A321873 Equals 3 * Sum_{k>=1} x^(k^2)*(1+x^k)/(1-x^k) where x = 1/4.
%e A321873 1.263293058100271331887972663903139146884324008972346213817762390...
%p A321873 evalf[130](sum(3/(4^k-1),k=1..infinity)); # _Muniru A Asiru_, Dec 20 2018
%t A321873 RealDigits[Sum[3/(4^k-1), {k, 1, Infinity}], 10, 120][[1]] (* _Amiram Eldar_, Nov 21 2018 *)
%o A321873 (PARI) suminf(k=1, 3/(4^k-1)) \\ _Michel Marcus_, Nov 20 2018
%Y A321873 Cf. A002450, A065442 (base 2), A321872 (base 3).
%K A321873 nonn,cons
%O A321873 1,2
%A A321873 _A.H.M. Smeets_, Nov 20 2018