cp's OEIS Frontend

A282723 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic residues mod p.

%I A282723 #12 Apr 07 2017 12:58:22
%S A282723 1,22,76,430,767,1072,1577,2675,3930,4587,6520,7518,10761,12258,14809,
%T A282723 19527,23025,26811,29148,35247,41900,47844,52771,57938,61377,66944,
%U A282723 73845,76568,79940,83941,94088,102237,104781,114744,117470,134498,152678,161389,167881,181249,193377,204075,221598,228185
%N A282723 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic residues mod p.
%H A282723 Vincenzo Librandi, <a href="/A282723/b282723.txt">Table of n, a(n) for n = 1..2500</a>
%H A282723 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 A282723 with(numtheory):
%p A282723 Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[]; Th:=[];
%p A282723 for i1 from 1 to 300 do
%p A282723 p:=ithprime(i1);
%p A282723 if (p mod 8) = 3 then
%p A282723 ql:=0; qu:=0; q:=0; nl:=0; nu:=0; n:=0;
%p A282723 for j from 1 to p-1 do
%p A282723 if legendre(j,p)=1 then
%p A282723 q:=q+j;
%p A282723 if j<p/2 then ql:=ql+j; else qu:=qu+j; fi;
%p A282723 else
%p A282723 n:=n+j;
%p A282723 if j<p/2 then nl:=nl+j; else nu:=nu+j; fi;
%p A282723 fi;
%p A282723 od;
%p A282723 Ql:=[op(Ql),ql];
%p A282723 Qu:=[op(Qu),qu];
%p A282723 Q:=[op(Q),q];
%p A282723 Nl:=[op(Nl),nl];
%p A282723 Nu:=[op(Nu),nu];
%p A282723 N:=[op(N),n];
%p A282723 Th:=[op(Th),q+ql];
%p A282723 fi;
%p A282723 od:
%p A282723 Ql; Qu; Q; Nl; Nu; N; Th; # A282721 - A282727
%t A282723 Table[Table[Mod[a^2, p], {a, 1, (p-1)/2}]//Total, {p, Select[Prime[Range[100]], Mod[#, 8] == 3 &]}] (* _Vincenzo Librandi_, Feb 21 2017 *)
%Y A282723 Cf. A282035-A282043 and A282721-A282727.
%K A282723 nonn
%O A282723 1,2
%A A282723 _N. J. A. Sloane_, Feb 20 2017