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 A382565 #7 Apr 02 2025 06:35:03
%S A382565 4,1,1,6,8,5,8,4,8,5,4,5,8,1,8,0,5,1,7,3,8,7,6,1,0,5,3,2,7,5,5,4,8,0,
%T A382565 6,0,5,2,4,0,4,9,7,9,1,1,9,8,3,4,4,6,0,3,2,3,9,2,8,6,0,0,0,9,1,5,8,3,
%U A382565 5,0,5,7,7,5,0,2,4,2,2,9,2,1,7,6,0,7,8,3,3,4,6,2,4,1,5,5,0,7,6,9,0,1,2,7
%N A382565 Decimal expansion of Sum_{p prime} 1/((p - 1)^2*(p + 1)).
%H A382565 <a href="/wiki/Index_to_constants#Start_of_section_P">Index to constants which are prime zeta sums</a> {0,2,1}.
%F A382565 Equals -A136141/4 + A086242/2 - A179119/4.
%F A382565 Equals Sum_{k>=2} (k-1) * (P(2*k-1) + P(2*k)), where P is the prime zeta function. - _Amiram Eldar_, Apr 02 2025
%e A382565 0.411685848545818051738761053275548060524049791198344603239286000...
%o A382565 (PARI) sumeulerrat(1/((p-1)^2*(p+1))) \\ _Amiram Eldar_, Apr 02 2025
%Y A382565 Cf. A086242, A136141, A179119.
%K A382565 nonn,cons
%O A382565 0,1
%A A382565 _Artur Jasinski_, Mar 31 2025