A120628 Primes such that their double is 1 away from a prime number.

2, 3, 5, 7, 11, 19, 23, 29, 31, 37, 41, 53, 79, 83, 89, 97, 113, 131, 139, 157, 173, 179, 191, 199, 211, 229, 233, 239, 251, 271, 281, 293, 307, 331, 337, 359, 367, 379, 419, 431, 439, 443, 491, 499, 509, 547, 577, 593, 601, 607, 619, 641, 653, 659, 661, 683

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*2 = 38 which is one away from 37 which is prime.
13 is not in the table because 13*2 = 26 is one away from 25 and 27 both not 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

Crossrefs

Cf. A005382, A005384.

Programs

Mathematica

Select[Range[683], PrimeQ[#] && Or[PrimeQ[2 # - 1], PrimeQ[2 # + 1]] &]  (* Ant King, Dec 12 2010 *)
Select[Prime[Range[200]],AnyTrue[2#+{1,-1},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 26 2020 *)

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",") ) ) }