login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173037 Numbers n such that n-4, n-2, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Average n of the four primes in two twin prime pairs (n-4, n-2) and (n+2, n+4) which are linked by the cousin prime pair (n-2, 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 (n-1, 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(n-1). - Michel Marcus, May 19 2014

EXAMPLE

a(1) = 9 because 9-4 = 5 is prime, 9-2 = 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(n-4) && isprime(n-2) && 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

Juri-Stepan Gerasimov, Feb 07 2010

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 25 11:55 EDT 2017. Contains 288710 sequences.