A342569 Noncube addends k > 0 such that x^3 + k produces a new minimum of its Hardy-Littlewood constant.

2, 5, 6, 13, 15, 20, 34, 83, 174, 246, 911, 1065, 1084, 1455, 1490, 1546, 3674, 8644, 9556, 15287, 15378, 15826, 25670

Offset: 1

Author

Hugo Pfoertner, May 03 2021

Keywords

• nonn
• hard
• more

Comments

a(24) > 42500.

For more information and references see A331950.

Examples

			   n  a(n)   Hardy-Littlewood         np / (expected number of primes)
             constant (rounded)       obtained from Li((10^9)^3+a(n))
                        np (x<=10^9)  (similar to table in A331946)
   1     2   1.298539558  22009948    1.34597
   2     5   1.142678324  19372839    1.18470
   3     6   0.822719287  13944026    0.85272
   4    13   0.814418714  13802244    0.84405
   5    15   0.784789179  13305075    0.81364
  ...
  20 15287   0.422422003   7162493    0.43801
  21 15378   0.419380705   7108723    0.43472
  22 15826   0.416982640   7068923    0.43228
  23 25670   0.388993112   6597073    0.40343
		

Crossrefs

Cf. A331946, A331949 (similar for x^2+k), A331950, A342547.