A056909 Primes of the form k^2+6.

7, 31, 127, 367, 631, 967, 1231, 3727, 4231, 6247, 7927, 8287, 11887, 17167, 21031, 22807, 30631, 34231, 39607, 48847, 72367, 108247, 109567, 126031, 160807, 185767, 198031, 231367, 235231, 261127, 265231, 279847, 290527, 323767, 354031

Offset

1,1

Comments

a(n) mod 120 = 7 or 31 for all n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2400

Formula

a(n) = 36*A056910(n)^2 + 12*A056910(n) + 7.

a(n) >> n^2 log n. - Charles R Greathouse IV, Nov 06 2024

Example

a(2)=127 since 11^2+6=127 which is prime.

Mathematica

Intersection[Table[n^2+6, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=6, i<=6, a={}; Do[If[PrimeQ[n^2+i], AppendTo[a, n^2+i]], {n, 0, 100}]; Print["n^2+", i, ", ", a]; i++ ] - Vladimir Joseph Stephan Orlovsky, Apr 29 2008
Select[Table[n^2+6, {n, 0, 7000}], PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

Prog

(Magma) [a: n in [0..700] | IsPrime(a) where a is n^2+6]; // Vincenzo Librandi, Nov 30 2011
(PARI) list(lim)=my(v=List(), t); forstep(k=1, sqrtint(lim\1-6), 2, if(isprime(t=k^2+6), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Nov 06 2024

Crossrefs

Cf. A002496, A056899, A049423, A005473, A056905.

Sequence in context: A327497 A036280 A153005 * A002147 A169785 A255282

Adjacent sequences: A056906 A056907 A056908 * A056910 A056911 A056912

Keyword

nonn,easy

Author

Henry Bottomley, Jul 07 2000

Status

approved