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
Examples
3.31977317747142166532355685764988796646855...
References
- Henri Cohen, Number Theory, Vol II: Analytic and Modern Tools, Springer (Graduate Texts in Mathematics 240), 2007.
- Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 265-266.
Links
- 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.
- Lea Beneish and Christopher Keyes, How often does a cubic hypersurface have a rational point?, arXiv:2405.06584 [math.NT], 2024. See p. 23.
- David Broadhurst, Five families of rapidly convergent evaluations of zeta values, arXiv:2401.08997 [math.NT], 2024.
- Henri Cohen, High-precision calculation of Hardy-Littlewood constants, (1998).
- Henri Cohen, High precision computation of Hardy-Littlewood constants. [Cached pdf version, with permission]
- Stéphane Vinatier and William Reginald Alcorn, Mathematics as seen by an artist: Inspiring mathematical objects, Eur. Math. Soc. Mag. (2025) Vol. 135, 20-31. See p. 26.
Programs
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PARI
\\ See Belabas, Cohen link. Run as HardyLittlewood2(x^2+x+41)/2 after setting the required precision.
Extensions
More terms from Hugo Pfoertner, Jan 31 2020