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%I #15 Nov 09 2020 20:34:03
%S 3,33,60,138,315,390,663,1008,1425,1743,2280,2475,3108,3570,4323,4590,
%T 6045,8055,8418,9168,11610,12045,13398,14340,14823,15813,22425,23028,
%U 24885,26163,32310,33033,34503,35250,42333,43995,46548,49173,51870,52785,58443,60393,61380,66435,67470,70623
%N Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p that are < p/2.
%H Robert Israel, <a href="/A282039/b282039.txt">Table of n, a(n) for n = 1..10000</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:=[];
%p for i1 from 1 to 300 do
%p p:=ithprime(i1);
%p if (p mod 8) = 7 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 fi;
%p od:
%p Ql; Qu; Q; Nl; Nu; N; # A282039, A282040, A282041, A282039 again, A282042, A282043
%p # alternative:
%p g:= proc(t,p) if t < p/2 then t else 0 fi end proc;
%p f:= proc(n) local k;
%p add(g(k^2 mod n, n),k=1..n/2)
%p end proc:
%p P:= select(isprime, [seq(i,i=7..3000,8)]):
%p map(f,P); # _Robert Israel_, Nov 09 2020
%t sum[p_]:= Total[If[#<p/2 && JacobiSymbol[#, p] != 1, #, 0]& /@ Range[p-1]];
%t sum /@ Select[Range[7, 1100, 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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