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

1,1

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).

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<p/2 then ql:=ql+j; else qu:=qu+j; fi;
            else
                n:=n+j;
                if j<p/2 then nl:=nl+j; else nu:=nu+j; fi;
            fi;
        od;
        Ql:=[op(Ql), ql];
        Qu:=[op(Qu), qu];
        Q:=[op(Q), q];
        Nl:=[op(Nl), nl];
        Nu:=[op(Nu), nu];
        N:=[op(N), n];
    fi;
od:
Ql; Qu; Q; Nl; Nu; N; # 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 *)

Crossrefs

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A124557 A195213 A317370 * A027955 A124654 A267204

Adjacent sequences: A282038 A282039 A282040 * A282042 A282043 A282044

Keyword

nonn

Author

N. J. A. Sloane, Feb 20 2017

Status

approved