OFFSET
1,1
COMMENTS
For more information and references see A331950.
Cubic polynomials with no quadratic terms have a poor yield in generating primes compared to quadratic polynomials. This can be seen when comparing the Hardy-Littlewood constants HL for quadratic polynomials of the form x^2 + k (k given in A003521) where HL(x^2 + 1) = 1.3728..., HL (x^2 + 7) = 1.9730..., ..., HL(x^2 + 991027) = 4.1237..., whereas the best known result for the present sequence, a(8) only leads to HL(x^3 + 23602) = 1.7167...
EXAMPLE
n a(n) Hardy-Littlewood
constant (rounded)
1 2 1.298539558
2 3 1.390543939
3 17 1.442297580
4 74 1.451456320
5 165 1.589487813
6 205 1.637173422
7 2609 1.679828689
8 23602 1.716729673
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Apr 29 2021
STATUS
approved