A212603 a(n) is the smallest prime such that it and the previous two primes are all of the form x^2 + n * y^2.

101, 97, 163, 101, 3061, 1777, 113, 2617, 8353, 419, 4937, 8353, 3457, 34729, 8209, 2617, 53201, 2203, 4253, 12301, 54049, 991, 6803, 232801, 3061, 11491, 739, 2237, 32297, 68329, 857, 19801, 12853, 7411, 53299, 28081, 941, 14503, 20107, 88729, 23993, 23251

Offset: 1

Author

John L. Drost, May 22 2012

Keywords

• nonn

Examples

			a(2)=97 since 97 = 25 + 2*36, 89 = 81 + 2*4, 83 = 81 + 2*1.
		

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[#] &]]; i = 1; While[i < Length[t] - 1 && (t[[i]] + 1 < t[[i + 1]] ||  t[[i+1]] + 1 < t[[i+2]]), i++]; If[i < Length[t] - 1, again = False; ans = Prime[t[[i+2]]], lim = 10*lim]]; ans, {n, 42}] (* T. D. Noe, May 23 2012 *)