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Search: id:A078597
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| A078597 |
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Primes of the form p*(p+4)+2 where p and p+4 are primes. |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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?
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MATHEMATICA
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Select[ #(#+4)+2&/@Select[Prime/@Range[500], PrimeQ[ #+4]&], PrimeQ]
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PROGRAM
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(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.
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CROSSREFS
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Except for the term 23, this is a subset of A048880. A051779 is Seq(2, 2). A049002 is Seq(0, -2). A045637 is Seq(0, 4).
Sequence in context: A102109 A141974 A142650 this_sequence A116659 A139940 A052073
Adjacent sequences: A078594 A078595 A078596 this_sequence A078598 A078599 A078600
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 10 2002
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