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 A324833 #9 Mar 31 2025 10:01:16
%S A324833 1,2,9,0,3,8,9,2,5,8,9,7,8,0,7,5,5,6,4,9,7,4,3,4,8,6,3,4,8,1,7,7,5,8,
%T A324833 7,7,6,3,8,4,9,3,2,1,4,1,9,9,2,0,5,6,8,8,3,0,0,4,1,2,7,0,4,5,6,3,9,8,
%U A324833 0,6,6,5,7,3,0,9,1,7,0,3,9,8,9,9,9,7,1,6,7,7,8,3,5,9,8,1,9,3,4,3,8
%N A324833 Decimal expansion of eta_2, a constant related to the asymptotic density of certain sets of residues.
%H A324833 Carl Pomerance, Andrzej Schinzel, <a href="http://mjcnt.phystech.edu/en/article.php?id=4">Multiplicative Properties of Sets of Residues</a>, Moscow Journal of Combinatorics and Number Theory. 2011. Vol. 1. Iss. 1. pp. 52-66. See p. 62.
%H A324833 <a href="/wiki/Index_to_constants#Start_of_section_P">Index to constants which are prime zeta sums</a> {0,2,2}
%F A324833 Sum_{p prime} 1/(p^2-1)^2.
%F A324833 Sum_{n>0} n P(2n+2) where P is the prime zeta P function.
%F A324833 Equals - A136141/4 + A086242/4 - A179119/4 + A382554/4. - _Artur Jasinski_, Mar 31 2025
%e A324833 0.12903892589780755649743486348177587763849321419920568830041270456398...
%t A324833 digits = 101; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[eta2 = Sum[n PrimeZetaP[2n + 2], {n, 1, m}], 10, digits][[1]]; rd[m0]; rd[m = 2m0]; While[rd[m] != rd[m-m0], Print[m]; m = m+m0]; Print[N[eta2, digits] ]; rd[m]
%Y A324833 Cf. A154945 (eta_1), A324834 (eta_3), A324835 (eta_4), A324836 (eta_5).
%K A324833 nonn,cons
%O A324833 0,2
%A A324833 _Jean-François Alcover_, Mar 17 2019