A138375 Primes of the form k^2 + 13.

13, 17, 29, 113, 157, 269, 337, 797, 1613, 1777, 1949, 2129, 3613, 4637, 5197, 6737, 7069, 7757, 8849, 11677, 12113, 13009, 13469, 14897, 15889, 20177, 20749, 23117, 24977, 32413, 36877, 37649, 39217, 40013, 48413, 49297, 69709, 70769, 71837, 79537, 80669, 87629

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 07 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..4500

Crossrefs

Cf. A113536, A241749.

Programs

Magma

[a: n in [0..700] | IsPrime(a) where a is n^2+13]; // Vincenzo Librandi, Nov 30 2011

Mathematica

Intersection[Table[n^2+13,{n,0,10^2}],Prime[Range[9*10^3]]] ...or... For[i=13,i<=13,a={};Do[If[PrimeQ[n^2+i],AppendTo[a,n^2+i]],{n,0,100}];Print["n^2+",i,",",a];i++ ]
Select[Table[n^2+13,{n,0,7000}],PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

Formula

a(n) = A241749(A113536(n)). - Elmo R. Oliveira, Apr 20 2025