A027863 Numbers k such that k^2 + (k+1)^2 + (k+2)^2 is prime.

0, 2, 6, 12, 14, 24, 34, 52, 56, 62, 66, 76, 86, 94, 96, 122, 124, 132, 152, 154, 164, 182, 184, 194, 206, 216, 226, 244, 252, 254, 262, 272, 276, 294, 322, 336, 342, 362, 364, 376, 384, 404, 406, 416, 436, 446, 464, 472, 486, 502, 546, 556, 584, 604, 612, 616

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• easy

Comments

No positive terms == {0,8} (mod 10). Numbers k such that both k and k+2 are terms: 12, 94, 122, 152, 182, 252, 362, 204, ... Numbers k such that k, k+2 and k+4 are terms: 1942, 7222, 7402, 15692, 23502, 30182, ... - Zak Seidov, Aug 22 2014

Links

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

Crossrefs

Cf. A027864 (associated primes).

Programs

Magma

[n: n in [0..1000] |IsPrime(n^2+(n+1)^2+(n+2)^2)]; // Vincenzo Librandi, Nov 18 2010

Maple

select(t -> isprime(t^2+(t+1)^2+(t+2)^2), [$0..1000]); # Robert Israel, Aug 22 2014

Mathematica

Select[Range[0,700],PrimeQ[Total[(#+{0,1,2})^2]]&] (* Harvey P. Dale, Apr 28 2012 *)

PARI

for(n=1,10^3,s=sum(i=0,2,(n+i)^2);if(isprime(s),print1(n,", "))) \\ Derek Orr, Aug 22 2014