The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A173037 Numbers k such that k-4, k-2, k+2 and k+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 k of the four primes in two twin prime pairs (k-4, k-2) and (k+2, k+4) which are linked by the cousin prime pair (k-2, k+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 (k-1, k, k+1) is always divisible by 7. - Fred Daniel Kline, Sep 24 2015 LINKS Klaus 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 From Jeppe Stig Nielsen, Feb 18 2020: (Start) For n >= 2, a(n) = 30*A014561(n-1) + 15. For n >= 2, a(n) = 10*A007811(n-1) + 5. a(n) = A007530(n) + 4. a(n) = A125855(n) + 5. (End) 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, 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, A007530, A007811, A014561, A023200, A046132, A087680, A112540, A125855, 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 29 15:50 EDT 2020. Contains 338066 sequences. (Running on oeis4.)