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%I #14 May 08 2021 22:58:54
%S 23,79,223,439,4759,53359,77839,95479,99223,159199,194479,239119,
%T 378223,416023,680623,2223079,2595319,2873023,3186223,3515623,4003999,
%U 5022079,6456679,6859159,8732023,9235519,9492559,10017223,10595023
%N Primes of the form p*(p+4)+2 where p and p+4 are primes.
%C More generally, if a and b are even numbers, let Seq(a,b) be the sequence of primes of the form p*(p+a)+b where p and p+a are primes. Seq(a,b) is finite if either a^2+b == 2 (mod 3) or a^2-4*b is a square. Is it infinite in all other cases?
%H Vincenzo Librandi, <a href="/A078597/b078597.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[ #(#+4)+2&/@Select[Prime/@Range[500], PrimeQ[ #+4]&], PrimeQ]
%o (PARI) prodtp(n1,n2,a,b)=local(f,x); f=0; forprime(x=n1,n2,if(isprime(x+a),f=x*(x+a)+b; if(isprime(f),print(x" "x+a" "f" "); ); ); ); \ Computes that part of Seq(a,b) with n1<=p<=n2.
%Y Except for the term 23, this is a subsequence of A048880. A051779 is Seq(2, 2). A049002 is Seq(0, -2). A045637 is Seq(0, 4).
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Dec 08 2002
%E Edited by _Dean Hickerson_, Dec 10 2002
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