%I #13 Nov 27 2017 11:35:24
%S 0,2,13,94,129,247,306,555,745,999,1579,1555,2466,2653,3059,4581,5430,
%T 6351,6658,8409,9087,11158,11996,12858,14814,15788,17880,17277,18950,
%U 19481,22400,24876,23518,27448,28115,32285,36743,38269,39851,43111,47406,50055,53683,51645,58274,66410,65119,76013,80465
%N Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p that are < p/2.
%H Jean-François Alcover, <a href="/A282724/b282724.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
%p # 2nd program
%p A282724 := proc(n)
%p local p,a,r;
%p p := A007520(n) ;
%p a := 0 ;
%p for r from 1 to (p-1)/2 do
%p if numtheory[legendre](r,p) <> 1 then
%p a := a+r ;
%p end if;
%p end do:
%p a ;
%p end proc:
%p seq(A282724(n),n=1..10) ; # _R. J. Mathar_, Apr 07 2017
%t b[1] = 3; b[n_] := b[n] = Module[{p}, p = NextPrime[b[n - 1]]; While[Mod[p, 8] != 3, p = NextPrime[p]]; p];
%t a[n_] := Module[{p, q, r}, p = b[n]; q = 0; For[r = 1, r <= (p - 1)/2, r++, If[KroneckerSymbol[r, p] != 1, q = q + r]]; q];
%t Array[a, 50] (* _Jean-François Alcover_, Nov 27 2017, after _R. J. Mathar_ *)
%Y Cf. A282035-A282043 and A282721-A282727.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 20 2017