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a(n) is the least number from 1,2,...,n-1, such that n!/a(n)+1 is prime, and a(n)=0, if such number does not exist.
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%I #15 Aug 03 2014 14:01:39

%S 1,1,2,2,3,2,2,5,6,1,8,2,5,7,2,3,0,5,8,4,16,3,8,4,10,1,13,8,2,19,4,11,

%T 11,7,3,1,12,13,4,1,24,2,8,5,9,25,16,2,12,0,26,0,17,22,44,22,37,7,48,

%U 4,37,18,7,39,16,19,7,15,19,36,30,1,14,15,16,1

%N a(n) is the least number from 1,2,...,n-1, such that n!/a(n)+1 is prime, and a(n)=0, if such number does not exist.

%C The sequence of primes n!/a(n)+1, when a(n)>0, is increasing.

%t Table[s = Select[Range[n - 1], PrimeQ[n!/# + 1] &, 1]; If[s == {}, 0, s[[1]]], {n, 2, 100}] (* _T. D. Noe_, Feb 13 2012 *)

%Y Cf. A089136, A092265, A092965, A092969, A092970.

%K nonn

%O 2,3

%A _Vladimir Shevelev_, Feb 12 2012