A342549 -id:A342549 - cp's OEIS frontend

A342548 Factors k > 0 such that the polynomial k*x^3 + x^2 + 1 produces a record of its Hardy-Littlewood constant.

1, 3, 21, 69, 81, 99, 489, 8169

Offset: 1

Hugo Pfoertner, May 01 2021

For more information and references see A331950.

			  n  a(n)   Hardy-Littlewood
            constant (rounded)
  1     1   3.0750320679
  2     3   3.3225199464
  3    21   4.3206296013
  4    69   4.3659028300
  5    81   4.9042526822
  6    99   6.0219444490
  7   489   6.5115238241
  8  8169   6.7898774153

Cf. A331950, A342547, A342549.

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

Original entry on oeis.org

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

Offset: 1

Hugo Pfoertner, May 03 2021

a(21)>40000.
For more information and references see A331950.
4187=53*79 is the first nonprime term.

			   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

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

cp's OEIS Frontend

A342548 Factors k > 0 such that the polynomial k*x^3 + x^2 + 1 produces a record of its Hardy-Littlewood constant.

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