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%I #12 May 15 2023 16:08:19
%S 2,17,3,1481,5,149,569,2081,2339,5939831,11,33164857769
%N Least prime p such that 2x^2 + p produces primes for x=0..n-1 and composite for x=n.
%C Other known values: a(14)=272259344081 and a(29)=29. There are no other terms less than 10^12. The primes p = 3, 5, 11, and 29 produce p consecutive distinct primes because the imaginary quadratic field Q(sqrt(-2p)) has class number 2. Assuming the prime k-tuples conjecture, this sequence is defined for n>0.
%D Paulo Ribenboim, My Numbers, My Friends, Springer,2000, pp. 349-350.
%H R. A. Mollin, <a href="http://www.jstor.org/stable/2975080">Prime-producing quadratics</a>, Amer. Math. Monthly 104 (1997), 529-544.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%t PrimeRun[p_Integer] := Module[{k=0}, While[PrimeQ[2k^2+p], k++ ]; k]; nn=9; t=Table[0,{nn}]; cnt=0; p=1; While[cnt<nn, p=NextPrime[p]; n=PrimeRun[p]; If[n<=nn && t[[n]]==0, t[[n]]=p; cnt++ ]]; t
%Y Cf. A007641, A050265, A161008, A164926.
%K hard,nonn,more
%O 1,1
%A _T. D. Noe_, Sep 09 2009
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