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 A282468 #42 Sep 28 2023 16:56:04
%S A282468 1,4,4,7,1,5,5,8,6,6,8,8,7
%N A282468 Decimal expansion of the zeta function at 2 of every second prime number.
%C A282468 From _Husnain Raza_, Aug 30 2023: (Start)
%C A282468 Note that since p_n > n*log(n), we can place a bound on the tail of the sum:
%C A282468 Sum_{n >= N} (prime(2n))^(-2) <= Sum_{n >= N} (2*n*log(2n))^(-2) <= Integral_{x=N..oo} (2*x*log(2x))^(-2) dx.
%C A282468 Taking the sum over all primes < 10^12, we see that the constant lies between 0.14471558668870 and 0.14471558668873. (End)
%H A282468 Husnain Raza, <a href="/A282468/a282468.gp.txt">PARI program for calculating more digits</a>.
%F A282468 Equals Sum_{n>=1} 1/A031215(n)^2 = Sum_{n>=1} 1/prime(2n)^2.
%e A282468 1/3^2 + 1/7^2 + 1/13^2 + 1/19^2 + 1/29^2 + ... = 0.14471558...
%o A282468 (PARI) sum(n=1, 2500000, 1./prime(2*n)^2)
%o A282468 (PARI) \\ see Raza link
%Y A282468 Cf. A031215, A085548.
%Y A282468 Zeta functions at 2: A085548 (for primes), A275647 (for nonprimes), A013661 (for natural numbers), A117543 (for semiprimes), A131653 (for triprimes), A222171 (for even numbers), A111003 (for odd numbers).
%K A282468 nonn,cons,hard,more
%O A282468 0,2
%A A282468 _Terry D. Grant_, Apr 14 2017
%E A282468 a(8)-a(12) from _Husnain Raza_, Aug 31 2023