cp's OEIS Frontend

A321890 Primes of the form p^2 + 16 where p is prime.

%I A321890 #53 Oct 29 2024 14:17:27
%S A321890 41,137,857,977,1697,6257,7937,11897,22817,32057,36497,44537,52457,
%T A321890 78977,96737,151337,160817,177257,192737,249017,326057,361217,434297,
%U A321890 477497,491417,516977,546137,564017,591377,674057,737897,776177,885497,942857,982097,1018097
%N A321890 Primes of the form p^2 + 16 where p is prime.
%C A321890 Also primes of the form p^2 + q^4 where p and q are primes. The proof of the equivalence of the set of primes p^2 + q^4, where p and q are primes, with respect to this sequence, is the following: Exactly 1 of (p, q) giving a term is 2. q^4 + 4 is divisible by 5 and/or composite and gives no terms. - _David A. Corneth_, Nov 21 2018
%e A321890 41 is prime and 41 = 5^2 + 16, where 5 is prime, therefore 41 is a term.
%p A321890 select(isprime,[ithprime(p)^2+16$p=1..180]); # _Muniru A Asiru_, Nov 24 2018
%t A321890 Select[Prime[Range[100]]^2+16, PrimeQ] (* _Amiram Eldar_, Nov 21 2018 *)
%o A321890 (MiniZinc)
%o A321890 include "globals.mzn";
%o A321890 int: n = 1;
%o A321890 int: max_val = 1200000;
%o A321890 array[1..n+1] of var 2..max_val: x;
%o A321890 % primes between 2..max_valset of int:
%o A321890 prime = 2..max_val diff { i | i in 2..max_val, j in 2..ceil(sqrt(i)) where i mod j = 0} ;
%o A321890 set of int: primes;primes = prime union {2};
%o A321890 solve satisfy;
%o A321890 constraint all_different(x) /\ x[1] in primes /\ x[2] in primes /\
%o A321890 pow(x[1],2)+16= x[2] ;
%o A321890 output [ show(x)]
%o A321890 (PARI) upto(n) = my(res = List()); forprime(p = 3, sqrtint(n-16), if(isprime(p^2 + 16), listput(res, p^2 + 16))); res \\ _David A. Corneth_, Nov 21 2018
%K A321890 nonn,easy
%O A321890 1,1
%A A321890 _Pierandrea Formusa_, Nov 20 2018
%E A321890 More terms from _Amiram Eldar_, Nov 21 2018