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

30, 38, 54, 60, 68, 80, 90, 96, 120, 138, 146, 158, 164, 174, 180, 188, 206, 218, 240, 248, 258, 264, 270, 278, 290, 300, 324, 338, 344, 360, 366, 374, 380, 390, 396, 408, 416, 428, 440, 450, 456, 474, 486, 498, 510, 516, 530, 548, 554, 564, 570, 578, 584

Offset: 1

Author

Anthony Lawson, Jul 24 2007

Keywords

• nonn
• easy

Comments

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

Examples

			30-7 is prime but 30-3 and 30-5 are not. Therefore 30 is in the sequence.
90-7 = 83 is prime, but neither 90-3 = 87 nor 90-5= 85 is prime, hence 90 is a term.
88-7 = 81 is not prime, hence 88 is not in the sequence.
86-7 = 79 is prime and 86-3 = 83 is also prime, hence 86 is not in the sequence.
78-7 = 71 is prime and 78-5 = 73 is also prime, hence 78 is not in the sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[n: n in [10..600]| IsPrime(n-7) and not IsPrime(n-3) and not IsPrime(n-5)]; // Vincenzo Librandi, Jan 10 2013

Mathematica

Select[2*Range[4, 500], PrimeQ[ # - 7] && ! PrimeQ[ # - 3] && ! PrimeQ[ # - 5] &] (* Stefan Steinerberger *)

PARI

{forstep(n=2, 584, 2, if(isprime(n-7)&&!isprime(n-3)&&!isprime(n-5),print1(n, ",")))} /* Klaus Brockhaus, Jul 25 2007 */

Extensions

Edited, corrected and extended by Klaus Brockhaus and Stefan Steinerberger, Jul 24 2007