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

1,4

Links

Table of n, a(n) for n=1..82.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A103689.

Sequence in context: A126813 A056141 A246004 * A125961 A016681 A210625

Adjacent sequences: A103685 A103686 A103687 * A103689 A103690 A103691

Keyword

easy,nonn

Author

Pierre CAMI, Feb 12 2005

Extensions

Corrected by Harvey P. Dale, Sep 09 2014

Definition simplified by Derek Orr, Sep 09 2014

Status

approved