A282726 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p .

2, 33, 95, 473, 944, 1139, 1826, 2996, 4585, 5004, 6683, 8413, 11394, 13393, 16566, 20376, 23946, 27804, 30883, 36384, 45671, 50059, 56040, 62357, 62874, 69559, 75486, 81635, 82795, 88050, 97183, 104166, 112030, 118159, 120925, 138193, 156613, 167066, 173670, 187262, 196026, 206796, 226333, 242750

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:=[]; Th:=[];
for i1 from 1 to 300 do
p:=ithprime(i1);
if (p mod 8) = 3 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];
Th:=[op(Th), q+ql];
fi;
od:
Ql; Qu; Q; Nl; Nu; N; Th; # A282721 - A282727

Mathematica

Table[Table[Mod[a^2, p/2], {a, 1, (p-1)}]//Total, {p, Select[Prime[ Range[ 200]], Mod[#, 8] == 3 &]}] (* Vincenzo Librandi, Feb 22 2017 *)

Crossrefs

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A342620 A065647 A041127 * A097978 A334197 A156369

Adjacent sequences: A282723 A282724 A282725 * A282727 A282728 A282729

Keyword

nonn

Author

N. J. A. Sloane, Feb 20 2017

Status

approved