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A112540 Numbers n such that (15n-4; 15n-2; 15n+2; 15n+4) is a prime quadruplet. 4

%I

%S 1,7,13,55,99,125,139,217,231,377,629,867,1043,1049,1071,1203,1261,

%T 1295,1401,1485,1687,2115,2323,2919,3423,3689,4199,4481,4633,4815,

%U 5151,5313,5403,5515,5921,6523,6609,6741,7323,7769,7953,8147,9031,9611,10485,11047

%N Numbers n such that (15n-4; 15n-2; 15n+2; 15n+4) is a prime quadruplet.

%C Also (4p + 16)/60 such that (p, p + 2, p + 6 and p + 8) is a prime quadruplet for p >= 11. - _Michel Lagneau_, Jul 02 2012

%C The density of these four-prime groups is approximately equal to (log x)^-3.45 (but not (log x)^-4). - _Xueshi Gao_, Jun 01 2014

%C All of the terms of this sequence are either 1, 7 or 13 modulo 14. - _Rodolfo Ruiz-Huidobro_, Dec 27 2019

%H Dana Jacobsen, <a href="/A112540/b112540.txt">Table of n, a(n) for n = 1..10000</a>

%e n = 7 => 15 * 7 - 4 = 101, 15 * 7 - 2 = 103, 15 * 7 + 2 = 107, 15 * 7 + 4 = 109.

%p A112540:=n->`if`(isprime(15*n-4) and isprime(15*n-2) and isprime(15*n+2) and isprime(15*n+4),n,NULL); seq(A112540(n), n=1..20000); # _Wesley Ivan Hurt_, Jul 26 2014

%t Select[Range[6610], PrimeQ[15# - 4] && PrimeQ[15# - 2] && PrimeQ[15# + 2] && PrimeQ[15# + 4]&] (* _T. D. Noe_, Nov 16 2006 *)

%o (PARI) for(n=1, 1e4, if(isprime(15*n-4) && isprime(15*n-2) && isprime(15*n+2) && isprime(15*n+4), print1(n, ", "))) \\ _Felix Fröhlich_, Jul 26 2014

%o (Perl) use ntheory ":all"; say for map { (4*$_+16)/60 } sieve_prime_cluster(11,15*10000, 2,6,8); # _Dana Jacobsen_, Dec 15 2015

%o (MAGMA) [n: n in [0..2*10^4] | IsPrime(15*n-4) and IsPrime(15*n-2) and IsPrime(15*n+2) and IsPrime(15*n+4)]; // _Vincenzo Librandi_, Dec 28 2015

%Y Cf. A007530, A014561.

%K nonn,easy

%O 1,2

%A _Karsten Meyer_, Dec 16 2005

%E Corrected by _T. D. Noe_, Nov 16 2006

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Last modified November 27 15:11 EST 2020. Contains 338683 sequences. (Running on oeis4.)