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 A382854 #18 Aug 01 2025 09:20:05
%S A382854 1,5,3,4,2,6,4,0,9,7,2,0,0,2,7,3,4,5,2,9,1,3,8,3,9,3,9,2,7,0,9,1,1,7,
%T A382854 1,5,9,6,2,2,4,9,9,3,2,8,1,9,8,7,2,3,7,2,9,3,9,6,5,9,9,9,5,2,5,3,3,0,
%U A382854 3,1,8,9,0,1,5,1,5,2,6,4,2,1,9,7,0,6,8
%N A382854 Decimal expansion of (1-log(2))/2.
%D A382854 Hari M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2012. See eq. (493), p. 313.
%H A382854 Paolo Xausa, <a href="/A382854/b382854.txt">Table of n, a(n) for n = 0..10000</a>
%H A382854 I. S. Gradsteyn and I. M. Ryzhik, <a href="http://mathtable.com/gr/index.html">Table of integrals, series and products</a> (6th ed.), 2000, (eq. 0.238.2).
%F A382854 Equals Sum_{k>=1} (-1)^(k+1) / ((2*k-1) * 2*k * (2*k+1)).
%F A382854 Equals Sum_{k>=1} zeta(2*k)/((2*k+1)*4^k) (Srivastava and Choi, 2012). - _Amiram Eldar_, Aug 01 2025
%e A382854 0.15342640972002734529138393927091171596224993281987...
%p A382854 evalf[140]((1-log(2))/2); # _Alois P. Heinz_, Apr 07 2025
%t A382854 First[RealDigits[(1 - Log[2])/2, 10, 100]] (* _Paolo Xausa_, Apr 07 2025 *)
%o A382854 (PARI) (1-log(2))/2 \\ _Amiram Eldar_, Aug 01 2025
%Y A382854 Cf. A187832, A372858, A382884.
%K A382854 nonn,cons
%O A382854 0,2
%A A382854 _Sean A. Irvine_, Apr 06 2025