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

1,1

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

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 *)

Prog

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

Crossrefs

Cf. A096690, A096691.

Sequence in context: A152472 A117012 A162291 * A154304 A144640 A084069

Adjacent sequences: A095694 A095695 A095696 * A095698 A095699 A095700

Keyword

nonn,easy

Author

Giovanni Teofilatto, Jul 06 2004

Extensions

Extended by Ray Chandler, Jul 12 2004

Status

approved