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Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p that are > p/2.
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%I #11 Aug 31 2018 15:58:49

%S 4,59,126,285,679,953,1706,2675,3709,4269,5551,6480,8488,8858,11194,

%T 12212,15103,20665,23511,24153,30197,32733,38458,36913,42643,42032,

%U 59638,64987,70396,70887,85606,94192,95522,99930,123090,117932,130367,134436,141262,149395,169769,167663,175469

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

%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

%t sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] == 1, #, 0]& /@ Range[p-1]];

%t sum /@ Select[Range[7, 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