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%I #30 Sep 09 2024 13:43:29
%S 3,3,1,9,7,7,3,1,7,7,4,7,1,4,2,1,6,6,5,3,2,3,5,5,6,8,5,7,6,4,9,8,8,7,
%T 9,6,6,4,6,8,5,5,4,5,8,5,6,5,2,9,8,5,8,4,9,1,5,3,9,4,0,7,2,7,9,5,0,2,
%U 6,3,3,1,0,4,2,6,1,1,8,1,4,9,7,3,7,5,5
%N Hardy-Littlewood constant for x^2+x+41.
%D Henri Cohen, Number Theory, Vol II: Analytic and Modern Tools, Springer (Graduate Texts in Mathematics 240), 2007.
%H Christian Axler and Mehdi Hassani, <a href="http://math.colgate.edu/~integers/v53/v53.mail.html">Carleman's inequality over prime numbers</a>, Integers (2021) Vol. 21, #A53.
%H Karim Belabas and Henri Cohen, <a href="/A221712/a221712.gp.txt">Computation of the Hardy-Littlewood constant for quadratic polynomials</a>, PARI/GP script, 2020.
%H Lea Beneish and Christopher Keyes, <a href="https://arxiv.org/abs/2405.06584">How often does a cubic hypersurface have a rational point?</a>, arXiv:2405.06584 [math.NT], 2024. See p. 23.
%H David Broadhurst, <a href="https://arxiv.org/abs/2401.08997">Five families of rapidly convergent evaluations of zeta values</a>, arXiv:2401.08997 [math.NT], 2024.
%H Henri Cohen, <a href="http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi">High-precision calculation of Hardy-Littlewood constants</a>, (1998).
%H Henri Cohen, <a href="/A221712/a221712.pdf">High precision computation of Hardy-Littlewood constants</a>. [Cached pdf version, with permission]
%e 3.31977317747142166532355685764988796646855...
%o (PARI) \\ See Belabas, Cohen link. Run as HardyLittlewood2(x^2+x+41)/2 after setting the required precision.
%Y Cf. A005846, A056561, A202018, A221713, A319906, A331876, A331877.
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_, Jan 26 2013
%E More terms from _Hugo Pfoertner_, Jan 31 2020