A120637 Primes such that their triple is 2 away from a prime number.

3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97, 103, 113, 127, 137, 139, 149, 163, 167, 173, 181, 191, 193, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 271, 277, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367, 373, 383

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.

Examples

			19 is a prime and 19*3 = 57 which is two away from 59 which is prime.
31 is not in the table because 31*3 = 93 which is 2 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. A125272.

Programs

Mathematica

Select[Prime[Range[200]],PrimeQ[3#+2]||PrimeQ[3#-2]&] (* Harvey P. Dale, Aug 10 2011 *)

PARI

primepm2(n,k) { 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",") ) ) }

Formula

Union of A023208 and A088878.