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A212604 a(n) is the smallest prime such that it and the previous three primes are all of the form x^2 + n * y^2.

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%I A212604 #10 Dec 09 2017 04:00:44
%S A212604 409,577,1759,409,55049,1783,127,20873,12889,6529,4943,12889,3461,
%T A212604 138041,46411,20873,115013,7417,4919,158209,8490721,7177,15787,
%U A212604 4967401,55049,383393,76597,5273,252541,10448401,2543,577193
%N A212604 a(n) is the smallest prime such that it and the previous three primes are all of the form x^2 + n * y^2.
%e A212604 a(3)=1759 since 1759 = 676 + 3*361, 1753 = 25 + 3*576, 1747 = 1600 + 3*49, 1741 = 289 + 3*484 are all prime.
%t A212604 Table[again = True; lim = 10; While[again, lim2 = lim/Sqrt[n];  t = PrimePi[Select[Union[Flatten[Table[x^2 + n y^2, {x, 0, lim}, {y, 0, lim2}]]], # < lim^2 && PrimeQ[#] &]]; pos = Position[Partition[Differences[t], 3, 1], {1, 1, 1}, 1, 1] ; If[pos != {}, again = False; ans = Prime[t[[pos[[1,1]] + 3]]], lim = 10*lim]]; ans, {n, 20}] (* _T. D. Noe_, May 23 2012 *)
%K A212604 nonn
%O A212604 1,1
%A A212604 _John L. Drost_, May 22 2012