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%I #10 Apr 30 2021 10:59:09
%S 2,3,17,74,165,205,2609,23602
%N Addends k > 0 such that the polynomial x^3 + k produces a record of its Hardy-Littlewood constant.
%C For more information and references see A331950.
%C 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...
%e n a(n) Hardy-Littlewood
%e constant (rounded)
%e 1 2 1.298539558
%e 2 3 1.390543939
%e 3 17 1.442297580
%e 4 74 1.451456320
%e 5 165 1.589487813
%e 6 205 1.637173422
%e 7 2609 1.679828689
%e 8 23602 1.716729673
%Y Cf. A003521 (records for x^2+k), A331950.
%K nonn,hard,more
%O 1,1
%A _Hugo Pfoertner_, Apr 29 2021