A212602 - OEIS

A212602

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

%I #9 Dec 09 2017 19:09:18

%S 17,3,37,17,409,79,11,97,673,251,53,673,17,239,211,97,353,337,23,521,

%T 1213,97,173,4201,409,859,439,113,937,7369,293,2129,7573,569,571,673,

%U 41,1567,997,409,1601,337,47,401,1801,1783,1867,4201,197,499,733,1301

%N a(n) is the smallest prime such that it and the previous prime are both of the form x^2 + n * y^2.

%e a(1)=17 since 17 = 4^2 + 1^2. 13 = 3^2 + 2^2 and these are the smallest consecutive primes that are the sum of two squares.

%t 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] && t[[i]] + 1 < t[[i+1]], i++]; If[i < Length[t], again = False; ans = Prime[t[[i+1]]], lim = 10*lim]]; ans, {n, 60}] (* _T. D. Noe_, May 23 2012 *)

%K nonn

%O 1,1

%A _John L. Drost_, May 22 2012