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.

409, 577, 1759, 409, 55049, 1783, 127, 20873, 12889, 6529, 4943, 12889, 3461, 138041, 46411, 20873, 115013, 7417, 4919, 158209, 8490721, 7177, 15787, 4967401, 55049, 383393, 76597, 5273, 252541, 10448401, 2543, 577193

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Example

a(3)=1759 since 1759 = 676 + 3*361, 1753 = 25 + 3*576, 1747 = 1600 + 3*49, 1741 = 289 + 3*484 are all prime.

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], 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 *)

Crossrefs

Sequence in context: A345544 A345797 A139661 * A316934 A052354 A213079

Adjacent sequences: A212601 A212602 A212603 * A212605 A212606 A212607

Keyword

nonn

Author

John L. Drost, May 22 2012

Status

approved