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 A332708 #12 Feb 26 2020 09:00:28
%S A332708 1,3,21,231,879,1011,1089,1659,2751
%N A332708 Factors k >= 0 such that the polynomial x^2 + k*x + 1 produces a record of its Hardy-Littlewood constant.
%C A332708 a(10) > 80000.
%C A332708 See A331940 for more information on the Hardy-Littlewood constant. The polynomials described by this sequence have an increasing rate of generating primes.
%C A332708 The following table provides the record values of the Hardy-Littlewood constant C, together with the number of primes np generated by the polynomial P(x) = x^2 + a(n)*x + 1 for 1 <= x <= r = 10^8 and the actual ratio np*(P(r)/r)/Integral_{x=2..P(r)} 1/log(x) dx.
%C A332708 a(n) C np C from ratio
%C A332708 1 2.24147 6456835 2.31230
%C A332708 3 3.54661 10220078 3.65998
%C A332708 21 5.58679 16096923 5.76458
%C A332708 231 5.74156 16543757 5.92460
%C A332708 879 5.83722 16813676 6.02126
%C A332708 1011 5.92725 17073610 6.11435
%C A332708 1089 6.03701 17392675 6.22861
%C A332708 1659 6.04359 17413761 6.23617
%C A332708 2751 7.46622 21508374 7.70252
%D A332708 Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
%H A332708 Karim Belabas, Henri Cohen, <a href="/A221712/a221712.gp.txt">Computation of the Hardy-Littlewood constant for quadratic polynomials</a>, PARI/GP script, 2020.
%H A332708 Henri Cohen, <a href="/A221712/a221712.pdf">High precision computation of Hardy-Littlewood constants</a>, preprint, 1998. [pdf copy, with permission]
%Y A332708 Cf. A221712, A331940, A331945, A331946, A331947, A331948, A331949, A332707.
%K A332708 nonn,more
%O A332708 1,2
%A A332708 _Hugo Pfoertner_, Feb 20 2020