A130038 - OEIS

%I #13 Sep 08 2022 08:45:30

%S 30,38,54,60,68,80,90,96,120,138,146,158,164,174,180,188,206,218,240,

%T 248,258,264,270,278,290,300,324,338,344,360,366,374,380,390,396,408,

%U 416,428,440,450,456,474,486,498,510,516,530,548,554,564,570,578,584

%N Even numbers n such that n-7 is prime, but neither n-3 nor n-5 is prime.

%C Even numbers that are the sum of 7 and another prime number, but not the sum of 3 or 5 plus another prime.

%H Vincenzo Librandi, <a href="/A130038/b130038.txt">Table of n, a(n) for n = 1..1000</a>

%e 30-7 is prime but 30-3 and 30-5 are not. Therefore 30 is in the sequence.

%e 90-7 = 83 is prime, but neither 90-3 = 87 nor 90-5= 85 is prime, hence 90 is a term.

%e 88-7 = 81 is not prime, hence 88 is not in the sequence.

%e 86-7 = 79 is prime and 86-3 = 83 is also prime, hence 86 is not in the sequence.

%e 78-7 = 71 is prime and 78-5 = 73 is also prime, hence 78 is not in the sequence.

%t Select[2*Range[4, 500], PrimeQ[ # - 7] && ! PrimeQ[ # - 3] && ! PrimeQ[ # - 5] &] (* _Stefan Steinerberger_ *)

%o (PARI) {forstep(n=2, 584, 2, if(isprime(n-7)&&!isprime(n-3)&&!isprime(n-5),print1(n, ",")))} /* _Klaus Brockhaus_, Jul 25 2007 */

%o (Magma) [n: n in [10..600]| IsPrime(n-7) and not IsPrime(n-3) and not IsPrime(n-5)]; // _Vincenzo Librandi_, Jan 10 2013

%K nonn,easy

%O 1,1

%A _Anthony Lawson_, Jul 24 2007

%E Edited, corrected and extended by _Klaus Brockhaus_ and _Stefan Steinerberger_, Jul 24 2007