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 A372858 #18 Aug 05 2025 15:45:50
%S A372858 8,4,6,5,7,3,5,9,0,2,7,9,9,7,2,6,5,4,7,0,8,6,1,6,0,6,0,7,2,9,0,8,8,2,
%T A372858 8,4,0,3,7,7,5,0,0,6,7,1,8,0,1,2,7,6,2,7,0,6,0,3,4,0,0,0,4,7,4,6,6,9,
%U A372858 6,8,1,0,9,8,4,8,4,7,3,5,7,8,0,2,9,3
%N A372858 Decimal expansion of (1 + log(2))/2.
%H A372858 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A372858 Equals Integral_{x=2..oo} (log(x))/x^2 dx.
%F A372858 Equals log(A019798). - _Hugo Pfoertner_, Jun 09 2024
%F A372858 Integral log(x)/x^m dx = -x^(1-m) Sum_{k=0..1} log^(1-k)(x)/(m-1)^(k+1). - _R. J. Mathar_, Jun 21 2024
%e A372858 0.84657359027997265470861606072908828403775006...
%t A372858 s = Integrate[Log[x]/x^2, {x, 2, Infinity}]
%t A372858 d = N[s, 100]
%t A372858 First[RealDigits[d]]
%t A372858 N[1/2 (1 + Log[2]), 100]
%t A372858 RealDigits[(1+Log[2])/2,10,120][[1]] (* _Harvey P. Dale_, Aug 05 2025 *)
%o A372858 (PARI) log(2)/2+.5 \\ _Charles R Greathouse IV_, Nov 21 2024
%Y A372858 Cf. A019798, A372859, A372860, A372861.
%Y A372858 Essentially the same as A016655, A102047.
%K A372858 nonn,cons
%O A372858 0,1
%A A372858 _Clark Kimberling_, Jun 09 2024