A096691 -id:A096691 - cp's OEIS frontend

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

Giovanni Teofilatto, Jul 06 2004

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

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

Cf. A096690, A096691.

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

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 *)

Extended by Ray Chandler, Jul 12 2004

A096689 Numbers n such that 2n^2 + 3n + 3 is prime.

Original entry on oeis.org

0, 2, 4, 10, 16, 20, 26, 34, 40, 44, 46, 50, 62, 64, 74, 76, 80, 82, 86, 92, 94, 110, 122, 140, 160, 164, 170, 176, 182, 200, 202, 212, 214, 220, 224, 232, 236, 250, 262, 296, 302, 304, 310, 320, 322, 326, 332, 344, 346, 352, 392, 400, 404, 422, 424, 446, 452

Offset: 1

Ray Chandler, Jul 12 2004

nonn

All n are {2,4} (mod 6), as in A047235, because otherwise 2*n^2 + 3*n + 3 is a multiple of 2 or 3. - R. J. Mathar, Jul 17 2012

Cf. A095697, A096690, A096691.

f[n_]:=n^2+(n+1)^2+(n+2); lst={};Do[p=f[n];If[PrimeQ[p],AppendTo[lst,n]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 04 2009 *)
Select[Range[0,500],PrimeQ[2#^2+3#+3]&] (* Harvey P. Dale, Jul 19 2011 *)

is(n)=isprime(2*n^2+3*n+3) \\ Charles R Greathouse IV, May 22 2017

a(n) = A096691(n)*2.

A096690 k such that k-th prime is of the form 2n^2 + 3n + 3.

Original entry on oeis.org

2, 7, 15, 51, 103, 150, 227, 359, 468, 553, 597, 687, 995, 1050, 1355, 1412, 1554, 1620, 1758, 1982, 2058, 2722, 3260, 4167, 5290, 5522, 5904, 6274, 6657, 7886, 8039, 8764, 8909, 9374, 9676, 10307, 10628, 11801, 12847, 16003, 16605, 16811, 17425

Offset: 1

Ray Chandler, Jul 12 2004

nonn

A095697 indexed by A000040.

Cf. A095697, A096689, A096691.

cp's OEIS Frontend

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

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A096689 Numbers n such that 2n^2 + 3n + 3 is prime.

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A096690 k such that k-th prime is of the form 2n^2 + 3n + 3.

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