A120628 - OEIS

%I #17 Sep 26 2020 19:41:39

%S 2,3,5,7,11,19,23,29,31,37,41,53,79,83,89,97,113,131,139,157,173,179,

%T 191,199,211,229,233,239,251,271,281,293,307,331,337,359,367,379,419,

%U 431,439,443,491,499,509,547,577,593,601,607,619,641,653,659,661,683

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

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

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

%H Harvey P. Dale, <a href="/A120628/b120628.txt">Table of n, a(n) for n = 1..1000</a>

%e 19 is a prime and 19*2 = 38 which is one away from 37 which is prime.

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

%t Select[Range[683], PrimeQ[#] && Or[PrimeQ[2 # - 1], PrimeQ[2 # + 1]] &]  (* _Ant King_, Dec 12 2010 *)

%t Select[Prime[Range[200]],AnyTrue[2#+{1,-1},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 26 2020 *)

%o (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",") ) ) }

%Y Cf. A005382, A005384.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Aug 17 2006