|
|
A244452
|
|
Primes p such that p^2-2 and p^2+4 are also prime (i.e., initial members of prime triples (p, p^2-2, p^2+4)).
|
|
1
|
|
|
3, 5, 7, 13, 37, 47, 103, 233, 293, 313, 607, 677, 743, 1367, 1447, 2087, 2543, 3023, 3803, 3863, 4093, 4153, 4373, 4583, 4643, 4793, 4957, 5087, 5153, 5623, 5683, 5923, 6287, 7177, 7247, 7547, 7817, 8093, 8527, 9133, 9403
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
3 is in the sequence since it is the first member of the triple (3, 3^2-2, 3^2+4) and the resulting values in the triple (3, 7, 13) are all prime.
|
|
MATHEMATICA
|
Select[Prime[Range[1200]], AllTrue[#^2+{4, -2}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 28 2018 *)
|
|
PROG
|
(PARI) forprime(p=2, 10^4, if(isprime(p^2-2) && isprime(p^2+4), print1(p, ", ")))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|