

A164385


Composite numbers n such that n+4 and n4 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
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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(n4)]; // 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

JuriStepan Gerasimov, Aug 14 2009


EXTENSIONS

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


STATUS

approved



