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

Author

Juri-Stepan Gerasimov, Aug 14 2009

Keywords

• nonn

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

Examples

			a(1) = 5(prime)+4 = 13(prime)-4 = 9 (composite).
a(2) = 11(prime)+4 = 19(prime)-4 = 15 (composite).
		

Crossrefs

Cf. A002808, A023202, A087680.

Programs

Magma

[n: n in [8..2000] | IsPrime(n+4) and IsPrime(n-4)]; // Vincenzo Librandi, Apr 22 2015

Mathematica

Select[Range[8, 2000], PrimeQ[#+4] && PrimeQ[#-4] &] (* Vincenzo Librandi, Apr 22 2015 *)
Select[Range[9,5000],AllTrue[#+{4,-4},PrimeQ]&] (* Harvey P. Dale, Mar 23 2025 *)

Formula

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

Extensions

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