A342566 - OEIS

%I #6 May 05 2021 08:42:21

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

%T 15287,26447

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

%C a(21)>40000.

%C For more information and references see A331950.

%C 4187=53*79 is the first nonprime term.

%e    n  a(n)   Hardy-Littlewood         np / (expected number of primes)

%e              constant (rounded)       obtained from Li(a(n)*(10^9)^3+1)

%e                         np (x<=10^9)  (similar to table in A331946)

%e    1     2   2.597079115  43503785    2.69054

%e    2     3   2.085815908  34707483    2.16060

%e    3     5   1.428347905  23566489    1.47910

%e    4     7   1.290763004  21179402    1.33641

%e    5    11   1.241279598  20211462    1.28447

%e   ...

%e   18 12433   0.450506688   6582602    0.46462

%e   19 15287   0.422449638   6150009    0.43536

%e   20 26447   0.418323708   6045844    0.43130

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

%K nonn,hard,more

%O 1,1

%A _Hugo Pfoertner_, May 03 2021