A212602 a(n) is the smallest prime such that it and the previous prime are both of the form x^2 + n * y^2.

17, 3, 37, 17, 409, 79, 11, 97, 673, 251, 53, 673, 17, 239, 211, 97, 353, 337, 23, 521, 1213, 97, 173, 4201, 409, 859, 439, 113, 937, 7369, 293, 2129, 7573, 569, 571, 673, 41, 1567, 997, 409, 1601, 337, 47, 401, 1801, 1783, 1867, 4201, 197, 499, 733, 1301

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

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.

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] && 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 *)

Crossrefs

Sequence in context: A139728 A336485 A317317 * A174380 A040278 A254326

Adjacent sequences: A212599 A212600 A212601 * A212603 A212604 A212605

Keyword

nonn

Author

John L. Drost, May 22 2012

Status

approved