A164385 Composite numbers n such that n+4 and n-4 are both prime.

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

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].

A164383 INTERSECT A164384; A087680 INTERSECT A002808.

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

Table of n, a(n) for n=1..52.

Formula

a(n) = A023202(n+1)+4 = A087680(n+1). - Zak Seidov, Apr 22 2015

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

Cf. A002808, A023202, A087680.

Sequence in context: A082549 A013569 A129401 * A339519 A258813 A046353

Adjacent sequences: A164382 A164383 A164384 * A164386 A164387 A164388

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 14 2009

Extensions

65 removed, 337 changed to 237 etc. by R. J. Mathar, Aug 20 2009

Status

approved