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%I #10 Feb 21 2020 11:00:02
%S 2,3,7,13,19,31,79,151,211,331,499,631,751,991,1171,2011,2311,2671,
%T 3019,3931,4159,4951,5119,6451,7459,10651,18379,32971,48799,61051,
%U 78439,84319,162451,199411,230239,257371,404251,462331,529699,584791,640819
%N Nonsquare factors k > 0 such that k*x^2 - 1 produces a new minimum of its Hardy-Littlewood constant.
%C a(42) > 10^6.
%C See A331940 for more information on the Hardy-Littlewood constant. The polynomials described by this sequence are increasingly prime-avoiding.
%C The following table provides the minimum record values of C, together with the number of primes np generated by the polynomial P(x) = a(n)*x^2 - 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 a(n) C np C from ratio
%C 2 3.70011 10448345 3.81422
%C 3 2.07514 5794128 2.13869
%C 7 0.88360 2411224 0.91046
%C 13 0.87451 2344299 0.89971
%C .. ....... ....... .......
%C 584791 0.21378 445220 0.21860
%C 640819 0.21229 439946 0.21641
%D Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
%H 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 Henri Cohen, <a href="/A221712/a221712.pdf">High precision computation of Hardy-Littlewood constants</a>, preprint, 1998. [pdf copy, with permission]
%Y Cf. A221712, A331940, A331945, A331946, A331947.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Feb 10 2020
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