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 A342316 #24 Mar 06 2025 15:53:05
%S A342316 8,7,7,6,4,9,1,4,6,2,3,4,9,5,1,3,0,9,8,1,4,0,8,9,5,7,0,1,8,1,5,7,4,8,
%T A342316 7,4,0,2,3,0,8,4,5,6,5,3,2,7,2,9,7,6,5,6,3,6,6,7,9,2,2,8,6,6,6,0,5,1,
%U A342316 4,5,8,1,1,7,3,4,0,9,7,8,3,7,0,8,1,5,4,0,8,5,6,7,4,6,3,9,8,4,6,4,4,9
%N A342316 Decimal expansion of Pi/2 - log(2).
%D A342316 Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 2.5.2.n, pp. 186 and 223.
%F A342316 Equals (-log(4) - psi(1/4) + psi(3/4)) / 2, where psi(x) denotes the digamma function.
%F A342316 Equals -Integral_{x=0..1} log(x)/((1+x)*sqrt(1-x^2)) dx. - _Bernard Schott_, Apr 28 2021
%F A342316 Equals Sum_{k>=1} (-1)^(k+1)/(k*(2*k-1)). - _Amiram Eldar_, Jun 08 2021
%F A342316 From _Peter Bala_, Mar 05 2024: (Start)
%F A342316 Equals 2 * A196521.
%F A342316 Equals (10/3)*Integral_{x = 0..1} x/(2 - x^2*(1 - x)) dx.
%F A342316 Equals 5*Sum_{n >= 1} 1/(n*binomial(3*n,n)*2^n). The first 10 terms of the series gives the approximate value 0.87764914623(37...), correct to 11 decimal places. (End)
%e A342316 0.87764914623495130981408957018157487402308456532730...
%t A342316 RealDigits[N[Pi/2 - Log[2], 105]][[10]]
%o A342316 (PARI) Pi/2 - log(2) \\ _Michel Marcus_, Mar 14 2021
%Y A342316 Cf. A019669 (Pi/2), A002162 (log(2)), A196521.
%K A342316 nonn,cons
%O A342316 1,1
%A A342316 _Peter Luschny_, Mar 14 2021