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URL: https://oeis.org/A282037

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A282037
Let p = n-th prime == 3 mod 4; a(n) = (sum of quadratic nonresidues mod p) - (sum of quadratic residues mod p).
7
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
1,2
COMMENTS
Equals A282036 - A282035.
LINKS
Christian Aebi and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 [math.NT] (2015).
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 *)
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.
Sequence in context: A323109 A023267 A319224 * A050562 A321806 A057190
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 20 2017
STATUS
approved