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

1,1

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

Mathematica

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

Prog

(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.

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).

Sequence in context: A141974 A364148 A142650 * A280576 A160297 A210706

Adjacent sequences: A078594 A078595 A078596 * A078598 A078599 A078600

Keyword

easy,nonn

Author

Cino Hilliard, Dec 08 2002

Extensions

Edited by Dean Hickerson, Dec 10 2002

Status

approved