A240133 Least number k such that n!/k + 1 and n!/k - 1 are twin primes.

1, 2, 2, 3, 12, 12, 48, 8, 5, 54, 44, 6, 24, 39, 6, 81, 20, 30, 19, 25, 380, 28, 264, 50, 52, 250, 35, 385, 20, 77, 182, 405, 77, 605, 143, 720, 144, 722, 96, 713, 46, 403, 98, 4508, 90, 77, 560, 806, 64, 665, 2376, 1785, 893, 1235, 4278, 159, 66, 1326, 1806, 429, 475

Offset: 3

Author

Derek Orr, Apr 02 2014

Keywords

• nonn

Examples

			6!/1-1 (719) and 6!/1+1 (721) are not both prime. 6!/2-1 (359) and 6!/2+1 (361) are not both prime. 6!/3-1 (239) and 6!/3+1 (241) are both prime. thus, a(6) = 3.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 3..350

Crossrefs

Cf. A212281, A212282.

Programs

Mathematica

lnk[n_]:=Module[{nf=n!,k=1},While[!AllTrue[nf/k+{1,-1},PrimeQ],k++];k]; Array[lnk,70,3] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 18 2015 *)

PARI

f(n)=for(k=1,n!,if(floor(n!/k-1)==n!/k-1 && floor(n!/k+1)==n!/k+1,if(ispseudoprime(n!/k-1) && ispseudoprime(n!/k+1),return(k))))