%I A131652
%S A131652 3,7,59,83,89,113,367,379,467,593,907,1217,1699,1777,1951,2287,2383,
%T A131652 2999,3019,3121,4271,4817,5839,6481,6569,6719,9479,9743,14867,16103,
%U A131652 17443,17839,18523,19841,21803,22003,22147,24151,25391,26399
%N A131652 Primes p for which sum_{1 <= n < p} (n!|p) == 0 (mod p), where (n!|p) 
               is the Legendre symbol.
%H A131652 Robert G. Wilson v, <a href="b131652.txt">Table of n, a(n) for n = 1..117</
               a>.
%e A131652 7 is a term in the sequence because (1!|7) + (2!|7) + (3!|7) + (4!|7) 
               + (5!|7) + (6!|7) = (1|7) + (2|7) + (6|7) + (24|7) + (120|7) + (720|7) 
               = (1|7) + (2|7) + (6|7) + (3|7) + (1|7) + (6|7) = 1+1+(-1)+(-1)+1+(-1) 
               = 0.
%t A131652 fQ[n_] := Block[{p = Prime@n, s = 0, k = t = 1}, While[k < p, t = Mod[t*k, 
               p]; k++; s = s + JacobiSymbol[t, p]]; s == 0]; Do[m = n; If[fQ@n, 
               Print@Prime@n], {n, 4000}] - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Sep 17 2007
%t A131652 fQ[p_] := Mod[ Sum[ JacobiSymbol[ k!, p], {k, p - 1}], p] == 0; Do[ If[ 
               fQ@ Prime@ n, Print@ Prime@ n], {n, 3008}] - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Sep 17 2007
%Y A131652 Sequence in context: A144030 A130294 A100772 this_sequence A164895 A046859 
               A084289
%Y A131652 Adjacent sequences: A131649 A131650 A131651 this_sequence A131653 A131654 
               A131655
%K A131652 nonn
%O A131652 1,1
%A A131652 Chris Monico (c.monico(AT)ttu.edu), Sep 10 2007
%E A131652 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
%E A131652 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007