A096689 -id:A096689 - 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

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.

A096691 Numbers n such that 8n^2 + 6n + 3 is prime.

Original entry on oeis.org

0, 1, 2, 5, 8, 10, 13, 17, 20, 22, 23, 25, 31, 32, 37, 38, 40, 41, 43, 46, 47, 55, 61, 70, 80, 82, 85, 88, 91, 100, 101, 106, 107, 110, 112, 116, 118, 125, 131, 148, 151, 152, 155, 160, 161, 163, 166, 172, 173, 176, 196, 200, 202, 211, 212, 223, 226, 227, 245, 247

Offset: 1

Ray Chandler, Jul 12 2004

nonn

Cf. A095697, A096689, A096690.

f[n_]:=n^2+(n+1)^2+(n+2); lst={};Do[p=f[n];If[PrimeQ[p],AppendTo[lst,n/2]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 04 2009 *)
Select[Range[0,300],PrimeQ[8#^2+6#+3]&] (* Harvey P. Dale, Jun 11 2015 *)

is(n)=isprime(8*n^2+6*n+3) \\ Charles R Greathouse IV, May 22 2017

a(n) = A096689(n)/2.

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

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A096691 Numbers n such that 8n^2 + 6n + 3 is prime.

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