A095697 Primes of the form x^2 + y^2 + z, where x, y and z are three successive numbers.

3, 17, 47, 233, 563, 863, 1433, 2417, 3323, 4007, 4373, 5153, 7877, 8387, 11177, 11783, 13043, 13697, 15053, 17207, 17957, 24533, 30137, 39623, 51683, 54287, 58313, 62483, 66797, 80603, 82217, 90527, 92237, 97463, 101027, 108347, 112103

Offset: 1

Author

Giovanni Teofilatto, Jul 06 2004

Keywords

• nonn
• easy

Comments

Equivalently, primes of the form 2n^2 + 3n + 3, generated by the n in A096689.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A096690, A096691.

Programs

Magma

[a: n in [0..300] | IsPrime(a) where a is 2*n^2 + 3*n + 3]; // Vincenzo Librandi, Jul 17 2012

Mathematica

f[n_]:=n^2+(n+1)^2+(n+2); lst={};Do[p=f[n];If[PrimeQ[p],AppendTo[lst,p]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 04 2009 *)
Select[Table[2*n^2+3*n+3,{n,0,2000}],PrimeQ] (* Vincenzo Librandi, Jul 17 2012 *)
Select[#[[1]]^2+#[[2]]^2+#[[3]]&/@Partition[Range[0,300],3,1],PrimeQ] (* Harvey P. Dale, Apr 01 2023 *)

Extensions

Extended by Ray Chandler, Jul 12 2004