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A342547
Addends k > 0 such that the polynomial x^3 + k produces a record of its Hardy-Littlewood constant.
3
2, 3, 17, 74, 165, 205, 2609, 23602
OFFSET
1,1
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...
EXAMPLE
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.
Sequence in context: A085874 A055739 A220703 * A245799 A056794 A135726
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Apr 29 2021
STATUS
approved