%I #17 Aug 31 2018 15:58:36
%S 2,31,82,379,815,892,1520,2441,3840,4005,5104,6858,8928,10740,13507,
%T 15795,18516,21453,24225,27975,36584,38901,44044,49499,48060,53771,
%U 57606,64358,63845,68569,74783,79290,88512,90711,92810,105908,119870,128797,133819,144151,148620,156741,172650,191105
%N Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2.
%H Robert Israel, <a href="/A282725/b282725.txt">Table of n, a(n) for n = 1..1000</a>
%H Aebi, Christian, and Grant Cairns. <a href="http://arxiv.org/abs/1512.00896">Sums of Quadratic residues and nonresidues</a>, arXiv preprint arXiv:1512.00896 (2015).
%p with(numtheory):
%p Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[]; Th:=[];
%p for i1 from 1 to 300 do
%p p:=ithprime(i1);
%p if (p mod 8) = 3 then
%p ql:=0; qu:=0; q:=0; nl:=0; nu:=0; n:=0;
%p for j from 1 to p-1 do
%p if legendre(j,p)=1 then
%p q:=q+j;
%p if j<p/2 then ql:=ql+j; else qu:=qu+j; fi;
%p else
%p n:=n+j;
%p if j<p/2 then nl:=nl+j; else nu:=nu+j; fi;
%p fi;
%p od;
%p Ql:=[op(Ql),ql];
%p Qu:=[op(Qu),qu];
%p Q:=[op(Q),q];
%p Nl:=[op(Nl),nl];
%p Nu:=[op(Nu),nu];
%p N:=[op(N),n];
%p Th:=[op(Th),q+ql];
%p fi;
%p od:
%p Ql; Qu; Q; Nl; Nu; N; Th; # A282721 - A282727
%t sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] != 1, #, 0]& /@ Range[p-1]];
%t sum /@ Select[Range[3, 1000, 8], PrimeQ] (* _Jean-François Alcover_, Aug 31 2018 *)
%Y Cf. A282035-A282043 and A282721-A282727.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Feb 20 2017
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