A282041 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p.

7, 92, 186, 423, 994, 1343, 2369, 3683, 5134, 6012, 7831, 8955, 11596, 12428, 15517, 16802, 21148, 28720, 31929, 33321, 41807, 44778, 51856, 51253, 57466, 57845, 82063, 88015, 95281, 97050, 117916, 127225, 130025, 135180, 165423, 161927, 176915, 183609, 193132, 202180, 228212, 228056, 236849

Offset: 1

Author

N. J. A. Sloane, Feb 20 2017

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2500
• Aebi, Christian, and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 (2015).

Crossrefs

Cf. A282035-A282043 and A282721-A282727.

Programs

Maple

with(numtheory):
Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[];
for i1 from 1 to 300 do
    p:=ithprime(i1);
    if (p mod 8) = 7 then
        ql:=0; qu:=0; q:=0; nl:=0; nu:=0; n:=0;
        for j from 1 to p-1 do
            if legendre(j, p)=1 then
                q:=q+j;
                if j
A282039, A282040, A282041, A282039 again, A282042, A282043

Mathematica

Table[Table[Mod[a^2, p], {a, 1, (p-1)/2}]//Total, {p, Select[Prime[Range[100]], Mod[#, 8] == 7 &]}] (* Vincenzo Librandi, Feb 21 2017 *)