A120639 Primes such that their quadruple is 1 away from a prime number.

2, 3, 5, 7, 11, 13, 17, 37, 41, 43, 53, 67, 71, 73, 79, 83, 97, 127, 131, 137, 139, 163, 173, 193, 197, 199, 227, 263, 277, 281, 293, 307, 373, 383, 409, 431, 433, 467, 487, 499, 503, 521, 563, 577, 587, 593, 617, 619, 673, 677, 683, 701, 709, 727, 739, 743, 797

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

			17*4 = 68, one away from 67 which is prime.
		

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Select[Prime[Range[200]],Or@@PrimeQ[4#+{1,-1}]&] (* Harvey P. Dale, Feb 18 2013 *)

PARI

primepm2(n,k) = \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",") ) ) }