A282037 - OEIS

%I #20 Aug 31 2018 15:59:03

%S 1,7,11,19,69,93,43,235,177,67,497,395,249,515,321,635,655,417,1057,

%T 163,1837,895,2483,1791,633,1561,1135,3585,1757,3419,2981,849,921,

%U 5909,993,1735,6821,3303,1137,6511,3771,9051,6585,2215,3241,3269,11975,3409,4419,1497,10563,2615,1641,5067,2855

%N Let p = n-th prime == 3 mod 4; a(n) = (sum of quadratic nonresidues mod p) - (sum of quadratic residues mod p).

%C Equals A282036 - A282035.

%H Rémy Sigrist, <a href="/A282037/b282037.txt">Table of n, a(n) for n = 1..10000</a>

%H Christian Aebi and Grant Cairns. <a href="http://arxiv.org/abs/1512.00896">Sums of Quadratic residues and nonresidues</a>, arXiv preprint arXiv:1512.00896 [math.NT] (2015).

%p with(numtheory):

%p a:=[]; m:=[]; d:=[];

%p for i1 from 1 to 200 do

%p p:=ithprime(i1);

%p if (p mod 4) = 3 then

%p sp:=0; sm:=0;

%p for j from 1 to p-1 do

%p if legendre(j,p)=1 then sp:=sp+j; else sm:=sm+j; fi; od;

%p a:=[op(a),sp]; m:=[op(m),sm]; d:=[op(d),sm-sp];

%p fi;

%p od:

%p a; m; d; # A282035, A282036, A282037

%t sum[p_] := Total[If[JacobiSymbol[#, p] == 1, -#, #]& /@ Range[p-1]];

%t sum /@ Select[Prime[Range[200]], Mod[#, 4] == 3&] (* _Jean-François Alcover_, Aug 31 2018 *)

%Y Sums of residues, nonresidues, and their differences, for p == 1 mod 4, p == 3 mod 4, and all p: A171555; A282035, A282036, A282037; A076409, A125615, A282038.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 20 2017