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A071406 a(n) is the smallest multiplier of n! such that -1+a(n)*n! and 1+a(n)*n! are both primes. 3

%I

%S 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,

%T 81,259,108,163,81,118,63,215,173,513,420,561,537,1162,158,33,122,286,

%U 459,391,305,288,114,307,15,680,355,365,338,70,23

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

%H Pierre CAMI, <a href="/A071406/b071406.txt">Table of n, a(n) for n = 1..300</a>

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

%t 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}]

%t 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 *)

%Y Cf. A063983, A071256, A060256.

%K nonn

%O 1,1

%A _Labos Elemer_, May 24 2002

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)