A353127 - OEIS

%I #22 Apr 25 2022 09:25:15

%S 1,7,7,4,2,5,3,9,1,9,7,1,2,3,9,4,3,4,5,2,9,1,3,9,0,6,2,8,5,1,0,8,6,1,

%T 2,1,5,7,5,2,9,2,4,7,1,7,4,4,9,9,4,2,4,0,2,4,8,2,6,5,7,3,3,4,5,6,1,6,

%U 1,7,5,8,3,6,3,5,1,0,6,5,9,5,1,4,4,5,8,0,0,2

%N Decimal expansion of Pi^2/4 - log(2).

%C Limit of the series u where u(n) = 1/n when n is a square, and u(n) = (-1)^n/n otherwise.

%D M. Lepez, Les Grands classiques de Mathématiques, Classes préparatoires scientifiques, Analyse, Exercices corrigés et commentés, MP-PC-PT, Bréal, 1995, Exercice 201, p. 29.

%F Equals A091476 - A002162.

%F Equals Sum_{k>=1} ( (-1)^k/k + 2/(2*k-1)^2 ).

%e 1.77425391971239434529139062851086121575292471744...

%p evalf(Pi^2/4 - log(2),100);

%t RealDigits[Pi^2/4 - Log[2], 10, 100][[1]] (* _Amiram Eldar_, Apr 24 2022 *)

%o (PARI) Pi^2/4 - log(2) \\ _Michel Marcus_, Apr 24 2022

%Y Cf. A091476 (Pi^2/4), A002162 (log(2)).

%K nonn,cons

%O 1,2

%A _Bernard Schott_, Apr 24 2022