A342566 Noncube factors k > 0 such that k*x^3 + 1 produces a new minimum of its Hardy-Littlewood constant.

2, 3, 5, 7, 11, 13, 29, 43, 83, 239, 463, 911, 1483, 1721, 3067, 4187, 10613, 12433, 15287, 26447

Offset

1,1

Comments

a(21)>40000.

For more information and references see A331950.

4187=53*79 is the first nonprime term.

Links

Table of n, a(n) for n=1..20.

Example

   n  a(n)   Hardy-Littlewood         np / (expected number of primes)
             constant (rounded)       obtained from Li(a(n)*(10^9)^3+1)
                        np (x<=10^9)  (similar to table in A331946)
   1     2   2.597079115  43503785    2.69054
   2     3   2.085815908  34707483    2.16060
   3     5   1.428347905  23566489    1.47910
   4     7   1.290763004  21179402    1.33641
   5    11   1.241279598  20211462    1.28447
  ...
  18 12433   0.450506688   6582602    0.46462
  19 15287   0.422449638   6150009    0.43536
  20 26447   0.418323708   6045844    0.43130

Crossrefs

Cf. A331946 (similar for k*x^2+1), A331950, A342549.

Sequence in context: A181525 A082843 A162567 * A067908 A236128 A332341

Adjacent sequences: A342563 A342564 A342565 * A342567 A342568 A342569

Keyword

nonn,hard,more

Author

Hugo Pfoertner, May 03 2021

Status

approved