This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078597 #14 May 08 2021 22:58:54 %S A078597 23,79,223,439,4759,53359,77839,95479,99223,159199,194479,239119, %T A078597 378223,416023,680623,2223079,2595319,2873023,3186223,3515623,4003999, %U A078597 5022079,6456679,6859159,8732023,9235519,9492559,10017223,10595023 %N A078597 Primes of the form p*(p+4)+2 where p and p+4 are primes. %C A078597 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 A078597 Vincenzo Librandi, <a href="/A078597/b078597.txt">Table of n, a(n) for n = 1..1000</a> %t A078597 Select[ #(#+4)+2&/@Select[Prime/@Range[500], PrimeQ[ #+4]&], PrimeQ] %o A078597 (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 A078597 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 A078597 easy,nonn %O A078597 1,1 %A A078597 _Cino Hilliard_, Dec 08 2002 %E A078597 Edited by _Dean Hickerson_, Dec 10 2002