A060256 Smallest multiple a(n) of n-th primorial q(n) such that a(n)*q(n)-1 and a(n)*q(n)+1 are a pair of twin primes.

2, 1, 1, 2, 1, 6, 8, 11, 4, 16, 22, 4, 74, 24, 37, 28, 14, 11, 242, 11, 91, 20, 83, 91, 35, 80, 48, 47, 226, 2, 12, 203, 30, 38, 356, 54, 266, 108, 305, 227, 173, 1185, 738, 13, 382, 277, 455, 433, 173, 1303, 926, 1162, 164, 298, 69, 121, 702, 1670, 36, 570, 170, 204

Offset: 1

Author

Labos Elemer, Mar 22 2001

Keywords

• nonn

Examples

			30030*j-1 or 30030*j+1 are not both primes for j=1,2,3,4,5. But for j=6 {180179,180181} are twin primes. So a(6)=6.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001359, A002110, A060229-A060232, A060255, A057706.

Programs

Mathematica

smp[n_]:=Module[{k=1},While[!PrimeQ[k*n+1]||!PrimeQ[k*n-1],k++];k]; Table[ smp[n],{n,FoldList[Times,Prime[Range[70]]]}] (* Harvey P. Dale, Oct 27 2016 *)

PARI

a(n)=p=vecprod(primes(n));for(k=1,+oo,ispseudoprime(k*p+1)&&ispseudoprime(k*p-1)&&return(k)) \\ Jeppe Stig Nielsen, Nov 09 2024

Extensions

Corrected and extended by Ray Chandler, Apr 03 2009