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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].

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. A000040, 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

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Last modified December 1 18:55 EST 2022. Contains 358475 sequences. (Running on oeis4.)