A103688 a(n) = n if A103689(n)*n +/- 1 are twin primes; a(n) = 0 otherwise.

0, 0, 0, 4, 0, 6, 0, 0, 9, 0, 0, 12, 0, 0, 15, 0, 0, 18, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 47, 0, 0, 0, 51, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 69, 0, 0, 72, 0, 0, 75, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Pierre CAMI, Feb 12 2005

Keywords

• easy
• nonn

Examples

			For n=5 2*5-1=9 is not prime, 2*5+1=11 is prime so a(5)=0.
For n=6 1*6-1=5 is prime, 1*6+1=7 is prime, 5 and 7 are twin primes so a(6)=6.
		

Crossrefs

Cf. A103689.

Programs

Mathematica

lktp[n_]:=Module[{k=1},While[NoneTrue[k*n+{1,-1},PrimeQ],k++];If[AllTrue[k*n+{1,-1},PrimeQ],n,0]]; Array[lktp,100] (* The program uses the functions NoneTrue and AllTrue from Mathematica version 10 *) (* Harvey P. Dale, Sep 09 2014 *)

PARI

a(n)=k=1;while(!isprime(k*n+1)&&!isprime(k*n-1),k++);k
for(n=1,100,if(isprime(a(n)*n+1)&&isprime(a(n)*n-1),print1(n,", "));print1(0,", ")) \\ Derek Orr, Sep 09 2014

Extensions

Corrected by Harvey P. Dale, Sep 09 2014

Definition simplified by Derek Orr, Sep 09 2014