A243451 - OEIS

%I #15 Sep 08 2022 08:46:08

%S 17,41,97,137,241,457,641,857,977,1697,2417,2617,3041,4241,5641,6257,

%T 6577,7937,8297,9041,9817,11897,13241,14177,14657,15641,16657,22817,

%U 27241,32057,36497,44537,47977,48857,52457,53377,60041,62017,70241,75641,78977,83537

%N Primes of the form n^2 + 16.

%C Intersection of A241751 and A028916; conjecture: sequence is infinite. - _Reinhard Zumkeller_, Apr 11 2015

%H Vincenzo Librandi, <a href="/A243451/b243451.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Table[n^2 + 16, {n, 0, 1000}], PrimeQ]

%t Select[Range[1,301,2]^2+16,PrimeQ] (* _Harvey P. Dale_, Nov 05 2015 *)

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

%o (Haskell)

%o a243451 n = a243451_list !! (n-1)

%o a243451_list = [x | x <- a241751_list, a010051' x == 1]

%o -- _Reinhard Zumkeller_, Apr 11 2015

%o (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

%Y Cf. A122062 (associated n).

%Y Cf. similar sequences listed in A243449.

%Y Cf. A010051, A241751; subsequence of A028916.

%Y 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).

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Jun 05 2014