A027866 Numbers k such that k^2 + (k+1)^2 + (k+2)^2 + (k+3)^2 + (k+4)^2 + (k+5)^2 is prime.

2, 3, 4, 9, 12, 13, 18, 19, 21, 23, 24, 32, 34, 38, 48, 51, 52, 56, 62, 63, 81, 82, 87, 96, 97, 102, 104, 109, 119, 128, 142, 146, 152, 158, 159, 164, 166, 167, 199, 212, 214, 217, 219, 221, 223, 224, 229, 233, 236, 238, 249, 251, 258, 269, 273, 277, 284, 291, 296

Offset: 1

Author

Patrick De Geest

Keywords

• nonn

Comments

Numbers k such that 55 + 30*k + 6*k^2 is prime. - Zak Seidov, May 20 2014

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Patrick De Geest, World!Of Numbers

Programs

Magma

[n: n in [0..400] | IsPrime(55+30*n+6*n^2)]; // Vincenzo Librandi, Nov 18 2010

Mathematica

Select[Range[6!], PrimeQ[#^2 + (# + 1)^2 + (# + 2)^2 + (# + 3)^2 + (# + 4)^2 + (# + 5)^2] &] (* Vladimir Joseph Stephan Orlovsky, Dec 20 2009 *)
Select[Range[300],PrimeQ[6#^2+30#+55]&] (* Harvey P. Dale, Oct 12 2022 *)

PARI

is(n)=isprime(n^2+(n+1)^2+(n+2)^2+(n+3)^2+(n+4)^2+(n+5)^2) \\ Charles R Greathouse IV, Feb 17 2017