A331941 - OEIS

%I #16 Nov 27 2024 07:03:08

%S 6,8,6,4,0,6,7,3,1,4,0,9,1,2,3,0,0,4,5,5,6,0,9,6,3,4,8,3,6,3,5,0,9,4,

%T 3,4,0,8,9,1,6,6,5,5,0,6,2,7,8,7,9,7,7,8,9,6,8,1,1,7,0,7,3,6,6,3,9,2,

%U 1,1,1,3,3,5,8,6,8,5,1,1,5,8,6,3,8,5,9

%N Hardy-Littlewood constant for the polynomial x^2 + 1.

%D Henri Cohen, Number Theory, Vol II: Analytic and Modern Tools, Springer (Graduate Texts in Mathematics 240), 2007.

%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.1, p. 85.

%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 Henri Cohen, <a href="/A221712/a221712.pdf">High-precision computation of Hardy-Littlewood constants</a>, (1998). [pdf copy, with permission]

%H Keith Conrad, <a href="https://kconrad.math.uconn.edu/articles/hlconst.pdf">Hardy-Littlewood Constants</a>, (2003).

%F Equals (1/2)*Product_{p=primes} (1 - Kronecker(-4,p)/(p - 1)).

%F Equals A199401/2.

%e 0.686406731409123004556096348363509434089166550627879778968117...

%o (PARI) \\ See Belabas, Cohen link. Run as HardyLittlewood2(x^2+1)/2 after setting the required precision.

%Y Cf. A002496, A005574, A083844, A199401, A206709, A221712.

%K nonn,cons

%O 0,1

%A _Hugo Pfoertner_, Feb 02 2020