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A270780 Let p_i = the i-th prime. a(i) is the smallest n>1 such that p_i divides n!-1.

%I A270780 #24 Jun 06 2017 17:42:25
%S A270780 3,5,9,11,5,17,4,10,15,35,39,41,45,15,18,42,48,35,17,77,41,21,43,99,
%T A270780 96,53,22,111,125,129,120,69,25,75,155,161,83,171,177,179,189,90,195,
%U A270780 81,105,111,82,227,101,28,239,125,255,261,267,135,236,279,141,291
%N A270780 Let p_i = the i-th prime. a(i) is the smallest n>1 such that p_i divides n!-1.
%C A270780 Since p divides (p-2)!-1, the i-th term a(i) cannot be much larger than i log i.
%H A270780 Alois P. Heinz, <a href="/A270780/b270780.txt">Table of n, a(n) for n = 3..5000</a>
%e A270780 For i=3, the third prime is 5, and 5 divides 3!-1.
%e A270780 The 7th prime is 17, and 17 divides 5!-1, so a(7)=5.
%p A270780 a:= proc(n) local k, p; p:=ithprime(n);
%p A270780       for k from 2 do if irem(k!, p)=1 then return k fi od
%p A270780     end:
%p A270780 seq(a(n), n=3..100);  # _Alois P. Heinz_, Mar 23 2016
%t A270780 snpd[p_]:=Module[{n=2},While[!Divisible[n!-1,p],n++];n]; Table[snpd[p],{p,Prime[Range[3,70]]}] (* _Harvey P. Dale_, Jun 06 2017 *)
%Y A270780 Cf. A000040, A002982, A270838.
%K A270780 nonn,look
%O A270780 3,1
%A A270780 _Peter Shor_, Mar 22 2016
%E A270780 More terms from _Alois P. Heinz_, Mar 23 2016