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A112540 Numbers n such that (15n-4; 15n-2; 15n+2; 15n+4) is a prime quadruplet. 4
1, 7, 13, 55, 99, 125, 139, 217, 231, 377, 629, 867, 1043, 1049, 1071, 1203, 1261, 1295, 1401, 1485, 1687, 2115, 2323, 2919, 3423, 3689, 4199, 4481, 4633, 4815, 5151, 5313, 5403, 5515, 5921, 6523, 6609, 6741, 7323, 7769, 7953, 8147, 9031, 9611, 10485, 11047, 11123, 11411, 12509, 12991, 13049, 13433, 13455, 14491, 15023, 16003, 16247, 16507, 16533, 17191, 17361, 17779, 17921, 18403 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

Dana Jacobsen, Table of n, a(n) for n = 1..10000

EXAMPLE

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

MAPLE

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

MATHEMATICA

Select[Range[6610], PrimeQ[15#-4] && PrimeQ[15#-2] && PrimeQ[15#+2] && PrimeQ[15#+4]&] (* T. D. Noe, Nov 16 2006 *)

PROG

(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

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

(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

CROSSREFS

Cf. A007530, A014561.

Sequence in context: A116522 A108056 A018562 * A193489 A091005 A015441

Adjacent sequences:  A112537 A112538 A112539 * A112541 A112542 A112543

KEYWORD

nonn,easy

AUTHOR

Karsten Meyer, Dec 16 2005

EXTENSIONS

Corrected by T. D. Noe, Nov 16 2006

STATUS

approved

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Last modified April 29 11:38 EDT 2017. Contains 285604 sequences.