A282725 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2.

2, 31, 82, 379, 815, 892, 1520, 2441, 3840, 4005, 5104, 6858, 8928, 10740, 13507, 15795, 18516, 21453, 24225, 27975, 36584, 38901, 44044, 49499, 48060, 53771, 57606, 64358, 63845, 68569, 74783, 79290, 88512, 90711, 92810, 105908, 119870, 128797, 133819, 144151, 148620, 156741, 172650, 191105

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

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

sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] != 1, #, 0]& /@ Range[p-1]];
sum /@ Select[Range[3, 1000, 8], PrimeQ] (* Jean-François Alcover, Aug 31 2018 *)

Crossrefs

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A175446 A054207 A104095 * A030459 A141978 A212569

Adjacent sequences: A282722 A282723 A282724 * A282726 A282727 A282728

Keyword

nonn

Author

N. J. A. Sloane, Feb 20 2017

Status

approved