A071406 a(n) is the smallest multiplier of n! such that -1+a(n)*n! and 1+a(n)*n! are both primes.

4, 2, 1, 3, 2, 17, 7, 6, 3, 14, 29, 30, 48, 27, 9, 24, 12, 97, 78, 47, 71, 80, 55, 13, 57, 20, 81, 259, 108, 163, 81, 118, 63, 215, 173, 513, 420, 561, 537, 1162, 158, 33, 122, 286, 459, 391, 305, 288, 114, 307, 15, 680, 355, 365, 338, 70, 23

Offset: 1

Author

Labos Elemer, May 24 2002

Keywords

• nonn

Examples

			n=7: a(7)=7, 7!=5040, 7.7!=35280 and {35279,35281} are primes.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A063983, A071256, A060256.

Programs

Mathematica

Table[fl=1; Do[s=(j!)*k; If[PrimeQ[s-1]&&PrimeQ[s+1]&&Equal[fl, 1], Print[{j, k}]; fl=0], {k, 1, 2*j^2}], {j, 0, 100}]
smnf[n_]:=Module[{k=1,f=n!},While[!PrimeQ[k*f+1]||!PrimeQ[k*f-1],k++]; k]; Array[smnf,60] (* Harvey P. Dale, May 24 2016 *)