cp's OEIS Frontend

A130038 Even numbers n such that n-7 is prime, but neither n-3 nor n-5 is prime.

%I A130038 #13 Sep 08 2022 08:45:30
%S A130038 30,38,54,60,68,80,90,96,120,138,146,158,164,174,180,188,206,218,240,
%T A130038 248,258,264,270,278,290,300,324,338,344,360,366,374,380,390,396,408,
%U A130038 416,428,440,450,456,474,486,498,510,516,530,548,554,564,570,578,584
%N A130038 Even numbers n such that n-7 is prime, but neither n-3 nor n-5 is prime.
%C A130038 Even numbers that are the sum of 7 and another prime number, but not the sum of 3 or 5 plus another prime.
%H A130038 Vincenzo Librandi, <a href="/A130038/b130038.txt">Table of n, a(n) for n = 1..1000</a>
%e A130038 30-7 is prime but 30-3 and 30-5 are not. Therefore 30 is in the sequence.
%e A130038 90-7 = 83 is prime, but neither 90-3 = 87 nor 90-5= 85 is prime, hence 90 is a term.
%e A130038 88-7 = 81 is not prime, hence 88 is not in the sequence.
%e A130038 86-7 = 79 is prime and 86-3 = 83 is also prime, hence 86 is not in the sequence.
%e A130038 78-7 = 71 is prime and 78-5 = 73 is also prime, hence 78 is not in the sequence.
%t A130038 Select[2*Range[4, 500], PrimeQ[ # - 7] && ! PrimeQ[ # - 3] && ! PrimeQ[ # - 5] &] (* _Stefan Steinerberger_ *)
%o A130038 (PARI) {forstep(n=2, 584, 2, if(isprime(n-7)&&!isprime(n-3)&&!isprime(n-5),print1(n, ",")))} /* _Klaus Brockhaus_, Jul 25 2007 */
%o A130038 (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 A130038 nonn,easy
%O A130038 1,1
%A A130038 _Anthony Lawson_, Jul 24 2007
%E A130038 Edited, corrected and extended by _Klaus Brockhaus_ and _Stefan Steinerberger_, Jul 24 2007