A243451 Primes of the form n^2 + 16.

17, 41, 97, 137, 241, 457, 641, 857, 977, 1697, 2417, 2617, 3041, 4241, 5641, 6257, 6577, 7937, 8297, 9041, 9817, 11897, 13241, 14177, 14657, 15641, 16657, 22817, 27241, 32057, 36497, 44537, 47977, 48857, 52457, 53377, 60041, 62017, 70241, 75641, 78977, 83537

Offset: 1

Author

Vincenzo Librandi, Jun 05 2014

Keywords

• nonn

Comments

Intersection of A241751 and A028916; conjecture: sequence is infinite. - Reinhard Zumkeller, Apr 11 2015

Links

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

Crossrefs

Cf. A122062 (associated n).

Cf. similar sequences listed in A243449.

Cf. A010051, A241751; subsequence of A028916.

Primes of form n^2+b^4, b fixed: A002496 (b=1), A256775 (b=3), A256776 (b=4), A256777 (b=5), A256834 (b=6), A256835 (b=7), A256836 (b=8), A256837 (b=9), A256838 (b=10), A256839 (b=11), A256840 (b=12), A256841 (b=13).

Programs

Haskell

a243451 n = a243451_list !! (n-1)
a243451_list = [x | x <- a241751_list, a010051' x == 1]
-- Reinhard Zumkeller, Apr 11 2015

Magma

[a: n in [0..1000] | IsPrime(a) where a is n^2+16];

Mathematica

Select[Table[n^2 + 16, {n, 0, 1000}], PrimeQ]
Select[Range[1,301,2]^2+16,PrimeQ] (* Harvey P. Dale, Nov 05 2015 *)

PARI

list(lim)=if(lim<17,return([])); my(v=List(),t); forstep(n=1,sqrtint(lim\1-16),2, if(isprime(t=n^2+16), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Aug 18 2017