A221712 Hardy-Littlewood constant for x^2+x+41.

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

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..87.

Christian Axler and Mehdi Hassani, Carleman's inequality over prime numbers, Integers (2021) Vol. 21, #A53.

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

David Broadhurst, Five families of rapidly convergent evaluations of zeta values, arXiv:2401.08997 [math.NT], 2024.

H. Cohen, High-precision calculation of Hardy-Littlewood constants, (1998).

Henri Cohen, High precision computation of Hardy-Littlewood constants. [Cached pdf version, with permission]

Example

3.31977317747142166532355685764988796646855...

Prog

(PARI) See Belabas, Cohen link. Run as HardyLittlewood2(x^2+x+41)/2 after setting the required precision.

Crossrefs

Cf. A005846, A056561, A202018, A221713, A319906, A331876, A331877.

Sequence in context: A262143 A284554 A078033 * A193741 A193824 A108075

Adjacent sequences: A221709 A221710 A221711 * A221713 A221714 A221715

Keyword

nonn,cons

Author

N. J. A. Sloane, Jan 26 2013

Extensions

More terms from Hugo Pfoertner, Jan 31 2020

Status

approved