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, 366031, 373327, 421207
Offset: 1
Examples
a(2)=127 since 11^2+6=127 which is prime.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..2400
Programs
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Magma
[a: n in [0..700] | IsPrime(a) where a is n^2+6]; // Vincenzo Librandi, Nov 30 2011
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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 *) -
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
Formula
a(n) >> n^2 log n. - Charles R Greathouse IV, Nov 06 2024
Comments