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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. 1

%I

%S 101,97,163,101,3061,1777,113,2617,8353,419,4937,8353,3457,34729,8209,

%T 2617,53201,2203,4253,12301,54049,991,6803,232801,3061,11491,739,2237,

%U 32297,68329,857,19801,12853,7411,53299,28081,941,14503,20107,88729,23993,23251

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

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

%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] - 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 *)

%K nonn

%O 1,1

%A _John L. Drost_, May 22 2012

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Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)