A331941 Hardy-Littlewood constant for the polynomial x^2 + 1.

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, 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, 1, 1, 1, 3, 3, 5, 8, 6, 8, 5, 1, 1, 5, 8, 6, 3, 8, 5, 9

Offset

0,1

References

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

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

Links

Table of n, a(n) for n=0..86.

Karim Belabas and Henri Cohen, Computation of the Hardy-Littlewood constant for quadratic polynomials, PARI/GP script, 2020.

Henri Cohen, High-precision computation of Hardy-Littlewood constants, (1998). [pdf copy, with permission]

Keith Conrad, Hardy-Littlewood Constants, (2003).

Formula

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

Equals A199401/2.

Example

0.686406731409123004556096348363509434089166550627879778968117...

Prog

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

Crossrefs

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

Sequence in context: A331374 A340725 A021597 * A169685 A339606 A360928

Adjacent sequences: A331938 A331939 A331940 * A331942 A331943 A331944

Keyword

nonn,cons

Author

Hugo Pfoertner, Feb 02 2020

Status

approved