

A173037


Numbers n such that n4, n2, n+2 and n+4 are prime.


5



9, 15, 105, 195, 825, 1485, 1875, 2085, 3255, 3465, 5655, 9435, 13005, 15645, 15735, 16065, 18045, 18915, 19425, 21015, 22275, 25305, 31725, 34845, 43785, 51345, 55335, 62985, 67215, 69495, 72225, 77265, 79695, 81045, 82725, 88815, 97845
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OFFSET

1,1


COMMENTS

Average n of the four primes in two twin prime pairs (n4, n2) and (n+2, n+4) which are linked by the cousin prime pair (n2, n+2).
All terms are odd composites; except for a(1) they are multiples of 5.
Subsequence of A087679, of A087680 and of A164385.
All terms except for a(1) are multiples of 15.  Zak Seidov, May 18 2014
One of (n1, n, n+1) is always divisible by 7.  Fred Daniel Kline, Sep 24 2015


LINKS

K. Brockhaus, Table of n, a(n) for n = 1..28388 (terms < 10^9).


FORMULA

For n >= 2, a(n) = 15*A112540(n1).  Michel Marcus, May 19 2014


EXAMPLE

a(1) = 9 because 94 = 5 is prime, 92 = 7 is prime, 9+2 = 11 is prime and 9+4 = 13 is prime.


MATHEMATICA

Select[Range[100000], AllTrue[#+{4, 2, 2, 4}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 30 2015 *)


PROG

(MAGMA) [ p+4: p in PrimesUpTo(100000)  IsPrime(p) and IsPrime(p+2) and IsPrime(p+6) and IsPrime(p+8) ]; // Klaus Brockhaus, Feb 09 2010
(PARI) is(n)=isprime(n4) && isprime(n2) && isprime(n+2) && isprime(n+4) \\ Charles R Greathouse IV, Sep 24 2015


CROSSREFS

Cf. A001359, A006512, A023200, A046132, A087680, A164385.
Sequence in context: A219129 A226927 A152219 * A029712 A136353 A136354
Adjacent sequences: A173034 A173035 A173036 * A173038 A173039 A173040


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Feb 07 2010


EXTENSIONS

Edited and extended beyond a(9) by Klaus Brockhaus, Feb 09 2010


STATUS

approved



