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

Offset: 1

Author

Hugo Pfoertner, Apr 29 2021

Keywords

• nonn
• hard
• more

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...

Examples

			  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

Cf. A003521 (records for x^2+k), A331950.