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

1,1

Comments

This sequence is a variation of the sequence in the reference. However this sequence should have an infinite number of terms.

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

Example

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.

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 *)

Prog

(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", ") ) ) }

Crossrefs

Cf. A005382, A005384.

Sequence in context: A078139 A347337 A210186 * A322471 A262837 A143260

Adjacent sequences: A120625 A120626 A120627 * A120629 A120630 A120631

Keyword

easy,nonn

Author

Cino Hilliard, Aug 17 2006

Status

approved