A027867 Primes of the form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2.

139, 199, 271, 811, 1279, 1459, 2539, 2791, 3331, 3919, 4231, 7159, 8011, 9859, 15319, 17191, 17839, 20551, 24979, 25759, 41851, 42859, 48079, 58231, 59419, 65539, 68071, 74611, 88591, 102199, 125299, 132331, 143239, 154579, 156511, 166351, 170371, 172399, 243631, 276079, 281251, 289099, 294391

Offset

1,1

Comments

Primes of form 55 + 30n + 6n^2. - Zak Seidov, May 20 2014

All terms == 1 or 19 (mod 30). - Robert Israel, Jul 18 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

P. De Geest, World!Of Numbers

Formula

a(n) = 55 + 30*m + 6*m^2 where m = A027866(n). - Zak Seidov, May 20 2014

Maple

select(isprime, [seq(6*t^2-30*t+55, t=6..1000)]); # Robert Israel, Jul 18 2017

Mathematica

lst={}; Do[a=n^2+(n+1)^2+(n+2)^2+(n+3)^2+(n+4)^2+(n+5)^2; If[PrimeQ[a], AppendTo[lst, a]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 02 2009 *)
Select[Table[Total[(n+Range[0, 5])^2], {n, 200}], PrimeQ] (* Harvey P. Dale, Jul 18 2011 *)
Select[Total/@Partition[Range[300]^2, 6, 1], PrimeQ] (* Harvey P. Dale, Jul 23 2021 *)

Crossrefs

Cf. A027866.

Sequence in context: A016067 A142524 A108383 * A140019 A107206 A256601

Adjacent sequences: A027864 A027865 A027866 * A027868 A027869 A027870

Keyword

nonn

Author

Patrick De Geest

Extensions

More terms from Robert Israel, Jul 18 2017

Status

approved