A282037 Let p = n-th prime == 3 mod 4; a(n) = (sum of quadratic nonresidues mod p) - (sum of quadratic residues mod p).

1, 7, 11, 19, 69, 93, 43, 235, 177, 67, 497, 395, 249, 515, 321, 635, 655, 417, 1057, 163, 1837, 895, 2483, 1791, 633, 1561, 1135, 3585, 1757, 3419, 2981, 849, 921, 5909, 993, 1735, 6821, 3303, 1137, 6511, 3771, 9051, 6585, 2215, 3241, 3269, 11975, 3409, 4419, 1497, 10563, 2615, 1641, 5067, 2855

Offset: 1

Author

N. J. A. Sloane, Feb 20 2017

Keywords

• nonn

Comments

Equals A282036 - A282035.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Christian Aebi and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 [math.NT] (2015).

Crossrefs

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.

Programs

Maple

with(numtheory):
a:=[]; m:=[]; d:=[];
for i1 from 1 to 200 do
p:=ithprime(i1);
if (p mod 4) = 3 then
sp:=0; sm:=0;
for j from 1 to p-1 do
if legendre(j,p)=1 then sp:=sp+j; else sm:=sm+j; fi; od;
a:=[op(a),sp]; m:=[op(m),sm]; d:=[op(d),sm-sp];
fi;
od:
a; m; d; # A282035, A282036, A282037

Mathematica

sum[p_] := Total[If[JacobiSymbol[#, p] == 1, -#, #]& /@ Range[p-1]];
sum /@ Select[Prime[Range[200]], Mod[#, 4] == 3&] (* Jean-François Alcover, Aug 31 2018 *)