A342547 - OEIS

A342547

Addends k > 0 such that the polynomial x^3 + k produces a record of its Hardy-Littlewood constant.

2, 3, 17, 74, 165, 205, 2609, 23602

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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...

LINKS

Table of n, a(n) for n=1..8.

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