A212605 a(n) is the smallest prime such that it and the previous four primes are all of the form x^2 + n * y^2.

2633, 587, 1777, 2633, 239521, 862471, 2017, 208457, 586273, 147451, 4951, 586273, 207073, 612553, 102871, 208457, 301681, 351439, 242447, 2076901, 55948657, 27487, 119503, 9425257, 239521, 5188507, 128467, 75853, 74049413

Offset: 1

Author

John L. Drost, May 22 2012

Keywords

• nonn

Examples

			a(7)=2017 since 2017 = 225 + 7*256, 2011 = 1444 + 7*81, 2003 = 1156 + 7*121, 1999 = 1936 + 7*9, and 1997 = 625 + 7*196 are all consecutive primes.
		

Programs

Mathematica

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], 4, 1], {1, 1, 1, 1}, 1, 1]; If[pos != {}, again = False; ans = Prime[t[[pos[[1, 1]] + 4]]], lim = 10*lim]]; ans, {n, 20}] (* T. D. Noe, May 23 2012 *)