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A342547
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Addends k > 0 such that the polynomial x^3 + k produces a record of its Hardy-Littlewood constant.
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3
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OFFSET
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1,1
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COMMENTS
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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...
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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