A120638 Primes such that their triple is not 2 away from a prime number.

2, 31, 41, 73, 101, 107, 109, 131, 151, 157, 179, 223, 229, 241, 281, 283, 311, 359, 379, 389, 421, 449, 463, 509, 521, 547, 563, 571, 599, 613, 617, 619, 631, 641, 647, 653, 661, 683, 691, 701, 719, 733, 739, 743, 773, 787, 809, 811, 821, 827, 829, 839, 857

Offset: 1

Author

Cino Hilliard, Aug 17 2006

Keywords

• easy
• nonn

Comments

This sequence is a variation of the sequence in the reference. However, this sequence should have an infinite number of terms. k=2 in the PARI code.

Examples

			31*3 = 93 which is two away from 91 and 95 both not prime.
		

References

• R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.18.

Crossrefs

Cf. A023208, A088878, A125272.

Programs

Mathematica

Select[Prime@Range@200,!PrimeQ[3#-2]&&!PrimeQ[3#+2]&] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2011 *)
Select[Prime[Range[200]],NoneTrue[3#+{2,-2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 01 2019 *)

PARI

primepm3(n,k) = =number of iterations,k = factor { local(x,p1,p2,f1,f2,r); if(k%2,r=2,r=1); for(x=1,n, p1=prime(x); p2=prime(x+1); if(!isprime(p1*k+r)&!isprime(p1*k-r), print1(p1",") ) ) }