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 A386711 #7 Jul 31 2025 06:58:57
%S A386711 2,9,2,4,5,3,6,3,4,3,4,4,5,6,0,8,2,7,9,1,6,4,1,4,2,1,8,5,5,3,1,8,1,1,
%T A386711 4,4,6,1,7,5,2,2,8,5,8,3,9,2,2,5,4,7,8,7,7,7,9,9,6,4,8,4,2,0,7,4,8,0,
%U A386711 0,4,4,0,6,8,3,9,0,7,2,6,6,8,3,6,7,8,3,1,6,9,7,1,8,1,7,2,4,2,7,6,2,0,6,7,8,6,2,9,7,5,0,4,6,2,1,2,1,3,1,3
%N A386711 Decimal expansion of Sum_{k>=2} (zeta(k)-1)/(k+1).
%D A386711 Hari M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2012. See eq. (500), p. 314.
%H A386711 Ovidiu Furdui, <a href="https://doi.org/10.1080/10652469.2015.1031129">The evaluation of a class of fractional part integrals</a>, Integral Transforms and Special Functions, Vol. 26, No. 8 (2015), pp. 635-641.
%H A386711 Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a>, 2011. See p. 348.
%H A386711 Hari M. Srivastava and Junesang Choi, <a href="https://link.springer.com/book/9789048157280">Series Associated with the Zeta and Related Functions</a>, Springer Science+Business Media Dordrecht, 2001. See eq. (474), p. 213.
%F A386711 Equals 3/2 - gamma/2 - log(2*Pi)/2 (Srivastava and Choi, 2001).
%F A386711 Equals -Sum_{k>=2} (k*log(1-1/k) + 1 + 1/(2*k)) (Shamos, 2011).
%e A386711 0.29245363434456082791641421855318114461752285839225...
%t A386711 RealDigits[3/2 - EulerGamma/2 - Log[2*Pi]/2, 10, 120][[1]]
%o A386711 (PARI) 3/2 - Euler/2 - log(2*Pi)/2
%Y A386711 Cf. A001620 (gamma), A061444.
%Y A386711 Sum_{k>=2} (zeta(k)-1)/(k+m): A153810 (m=0), this constant (m=1), A386712 (m=2).
%K A386711 nonn,cons
%O A386711 0,1
%A A386711 _Amiram Eldar_, Jul 31 2025