A078597 Primes of the form p*(p+4)+2 where p and p+4 are primes.

23, 79, 223, 439, 4759, 53359, 77839, 95479, 99223, 159199, 194479, 239119, 378223, 416023, 680623, 2223079, 2595319, 2873023, 3186223, 3515623, 4003999, 5022079, 6456679, 6859159, 8732023, 9235519, 9492559, 10017223, 10595023

Offset: 1

Author

Cino Hilliard, Dec 08 2002

Keywords

• easy
• nonn

Comments

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?

Links

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

Crossrefs

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).

Programs

Mathematica

Select[ #(#+4)+2&/@Select[Prime/@Range[500], PrimeQ[ #+4]&], PrimeQ]

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.

Extensions

Edited by Dean Hickerson, Dec 10 2002