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 A380547 #17 Jan 26 2025 20:30:36
%S A380547 4,2,7,7,2,7,9,3,2,6,9,3,9,7,8,2,2,1,3,2,1,1,1,6,6,1,9,1,3,9,6,7,1,2,
%T A380547 5,6,3,5,3,7,3,3,3,9,2,9,4,1,1,6,7,0,5,5,0,8,2,1,6,9,7,1,9,8,7,1,6,7,
%U A380547 1,6,3,7,9,8,9,7,2,0,1,3,3,9,7,4,5,0,7,7,0
%N A380547 Decimal expansion of the absolute value of the sum of the Dirichlet L-series A000035 at s=1/2.
%C A380547 Defined as L(s) = (1-2^(-s))*zeta(s) by analytic continuation of the Riemann zeta function.
%F A380547 Equals A268682*A059750.
%F A380547 Equals A010503 * A113024 = Sum_{n>=1} (-1)^(n+1)/sqrt(2*n). - _Amiram Eldar_, Jan 26 2025
%e A380547 Sum_{n>=1} A000035(n)/sqrt(n) = -0.42772793269397822132111661913967125635373339294116...
%t A380547 RealDigits[(1/Sqrt[2]-1)*Zeta[1/2], 10, 120][[1]] (* _Amiram Eldar_, Jan 26 2025 *)
%o A380547 (PARI) (1/sqrt(2)-1)*zeta(1/2) \\ _Amiram Eldar_, Jan 26 2025
%Y A380547 Cf. A111003 (s=2), A233091 (s=3), A300707 (s=4), A059750 (zeta(1/2)), A000035, A010503, A113024, A268682.
%K A380547 nonn,cons
%O A380547 0,1
%A A380547 _R. J. Mathar_, Jan 26 2025