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 A358516 #20 Jul 14 2025 10:22:32
%S A358516 0,5,2,9,6,1,0,2,7,7,8,6,5,5,7,2,8,5,5,0,1,1,3,0,9,0,9,5,8,3,0,1,9,8,
%T A358516 0,2,8,1,7,6,6,6,9,3,5,3,8,7,1,7,7,1,7,4,9,0,8,0,2,6,6,8,5,6,5,3,4,5,
%U A358516 3,9,1,0,6,0,6,0,5,6,0,9,7,8,7,8,3,9,3,3,2,0,6,5,9,5,0,4
%N A358516 Decimal expansion of Sum_{k >= 1} (-1)^(k+1)*1/((k+2)*(k+3)).
%H A358516 Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011) p.100.
%F A358516 Equals Sum_{k >= 1} (-1)^(k+1)*/((k+2)*(k+3)) = A016627 -4/3.
%F A358516 Equals 2*log(2) - 4/3 = Sum_{k >= 2} 1/(4*k^3 - k) = Sum_{k >= 1} (zeta(2*k + 1) - 1)/(4^k). [from the Shamos reference]
%F A358516 Equals Sum_{k >= 1} 1/((2^k)*(4*k + 12)). [from the Shamos reference]
%F A358516 Equals Sum_{k>=3} (-1)^(k+1)/A002378(k). - _Amiram Eldar_, Nov 21 2022
%e A358516 0.0529610277865572855011309095830198028176669353...
%t A358516 Join[{0}, RealDigits[2*Log[2] - 4/3, 10, 120][[1]]] (* _Amiram Eldar_, Nov 21 2022 *)
%o A358516 (PARI) 2*log(2) - 4/3
%Y A358516 Cf. A002378, A242023, A242024, A358517, A358519.
%Y A358516 Cf. A002162.
%K A358516 nonn,cons
%O A358516 0,2
%A A358516 _Claude H. R. Dequatre_, Nov 20 2022
%E A358516 Missing terms 6, 0 inserted after a(74) by _Georg Fischer_, Feb 07 2025