A282042 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2.

11, 128, 219, 520, 1176, 1348, 2221, 3310, 4766, 6106, 8034, 8271, 10049, 12443, 14613, 15193, 21012, 27486, 26814, 30664, 39248, 39318, 41699, 48888, 46052, 52595, 74613, 72878, 78599, 85768, 107895, 103643, 111125, 111195, 130497, 145619, 148490, 160159, 169503, 166856, 180406, 194204

Offset: 1

Author

N. J. A. Sloane, Feb 20 2017

Keywords

• nonn

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).

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

sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] != 1, #, 0]& /@ Range[p-1]];
sum /@ Select[Range[7, 1000, 8], PrimeQ] (* Jean-François Alcover, Aug 31 2018 *)