|
|
A164385
|
|
Composite numbers n such that n+4 and n-4 are both prime.
|
|
1
|
|
|
9, 15, 27, 33, 57, 63, 75, 93, 105, 135, 153, 177, 195, 237, 267, 273, 363, 393, 405, 435, 453, 483, 495, 567, 573, 597, 603, 657, 687, 705, 723, 747, 765, 825, 915, 933, 987, 1017, 1035, 1065, 1113, 1167, 1197, 1227, 1233, 1287, 1293, 1323, 1377, 1443, 1455, 1485
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Composite numbers of the form A023202(k)+4, any k.
A087680 without the {7} [Proof: there are no 3 primes in arithmetic progression p, p+4, p+8, except p=3].
If p=3*l+1, p+8 were divisible by 3, and if p=3*l+2, p+4 were divisible by 3. - R. J. Mathar, Aug 20 2009]
All terms are divisible by 3. - Zak Seidov, Apr 22 2015
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(1) = 5(prime)+4 = 13(prime)-4 = 9 (composite).
a(2) = 11(prime)+4 = 19(prime)-4 = 15 (composite).
|
|
MATHEMATICA
|
Select[Range[8, 2000], PrimeQ[#+4] && PrimeQ[#-4] &] (* Vincenzo Librandi, Apr 22 2015 *)
|
|
PROG
|
(Magma) [n: n in [8..2000] | IsPrime(n+4) and IsPrime(n-4)]; // Vincenzo Librandi, Apr 22 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
65 removed, 337 changed to 237 etc. by R. J. Mathar, Aug 20 2009
|
|
STATUS
|
approved
|
|
|
|