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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A326407 A126127 A230324 * A103899 A093324 A169676

Adjacent sequences: A060253 A060254 A060255 * A060257 A060258 A060259

Keyword

nonn

Author

Labos Elemer, Mar 22 2001

Extensions

Corrected and extended by Ray Chandler, Apr 03 2009

Status

approved