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%I #16 Apr 01 2023 11:34:42
%S 3,17,47,233,563,863,1433,2417,3323,4007,4373,5153,7877,8387,11177,
%T 11783,13043,13697,15053,17207,17957,24533,30137,39623,51683,54287,
%U 58313,62483,66797,80603,82217,90527,92237,97463,101027,108347,112103
%N Primes of the form x^2 + y^2 + z, where x, y and z are three successive numbers.
%C Equivalently, primes of the form 2n^2 + 3n + 3, generated by the n in A096689.
%H Vincenzo Librandi, <a href="/A095697/b095697.txt">Table of n, a(n) for n = 1..1000</a>
%t 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 *)
%t Select[Table[2*n^2+3*n+3,{n,0,2000}],PrimeQ] (* _Vincenzo Librandi_, Jul 17 2012 *)
%t Select[#[[1]]^2+#[[2]]^2+#[[3]]&/@Partition[Range[0,300],3,1],PrimeQ] (* _Harvey P. Dale_, Apr 01 2023 *)
%o (Magma) [a: n in [0..300] | IsPrime(a) where a is 2*n^2 + 3*n + 3]; // _Vincenzo Librandi_, Jul 17 2012
%Y Cf. A096690, A096691.
%K nonn,easy
%O 1,1
%A _Giovanni Teofilatto_, Jul 06 2004
%E Extended by _Ray Chandler_, Jul 12 2004
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