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

3,2

Links

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

Example

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.

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 *)

Prog

(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))))

Crossrefs

Cf. A212281, A212282.

Sequence in context: A182779 A199673 A335942 * A293445 A126339 A268725

Adjacent sequences: A240130 A240131 A240132 * A240134 A240135 A240136

Keyword

nonn

Author

Derek Orr, Apr 02 2014

Status

approved