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%I #9 Feb 19 2020 22:03:24
%S 1,5,11,17,29,41,89,101,461,521,761,941,1091,1361,1889,2141,3449,4289,
%T 5381,5561,10709,15461,23201,59309,70769,134741,174929,329969,493349
%N Factors k > 0 such that k*x^2 + 1 produces a new minimum of its Hardy-Littlewood constant.
%C a(30) > 600000.
%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 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 1 1.37281 3954181 1.41606
%C 5 0.66031 1816520 0.67979
%C 11 0.56115 1512897 0.57810
%C 17 0.52244 1392498 0.53816
%C .. ....... ...... .......
%C 329969 0.20443 430342 0.20883
%C 493349 0.20348 424719 0.20781
%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, A331947, A331948.
%K nonn,more
%O 1,2
%A _Hugo Pfoertner_, Feb 10 2020
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