cp's OEIS Frontend

A282043 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p.

%I A282043 #14 Aug 30 2018 15:22:16
%S A282043 14,161,279,658,1491,1738,2884,4318,6191,7849,10314,10746,13157,16013,
%T A282043 18936,19783,27057,35541,35232,39832,50858,51363,55097,63228,60875,
%U A282043 68408,97038,95906,103484,111931,140205,136676,145628,146445,172830,189614,195038,209332,221373,219641,238849,254597
%N A282043 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p.
%H A282043 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 A282043 with(numtheory):
%p A282043 Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[];
%p A282043 for i1 from 1 to 300 do
%p A282043 p:=ithprime(i1);
%p A282043 if (p mod 8) = 7 then
%p A282043 ql:=0; qu:=0; q:=0; nl:=0; nu:=0; n:=0;
%p A282043 for j from 1 to p-1 do
%p A282043 if legendre(j,p)=1 then
%p A282043 q:=q+j;
%p A282043 if j<p/2 then ql:=ql+j; else qu:=qu+j; fi;
%p A282043 else
%p A282043 n:=n+j;
%p A282043 if j<p/2 then nl:=nl+j; else nu:=nu+j; fi;
%p A282043 fi;
%p A282043 od;
%p A282043 Ql:=[op(Ql),ql];
%p A282043 Qu:=[op(Qu),qu];
%p A282043 Q:=[op(Q),q];
%p A282043 Nl:=[op(Nl),nl];
%p A282043 Nu:=[op(Nu),nu];
%p A282043 N:=[op(N),n];
%p A282043 fi;
%p A282043 od:
%p A282043 Ql; Qu; Q; Nl; Nu; N; # A282039, A282040, A282041, A282039 again, A282042, A282043
%t A282043 sqnr[p_] := Select[Range[p-1], JacobiSymbol[#, p] != 1&] // Total;
%t A282043 sqnr /@ Select[Prime[Range[200]], Mod[#, 8] == 7&] (* _Jean-François Alcover_, Aug 30 2018 *)
%Y A282043 Cf. A282035-A282042 and A282721-A282727.
%K A282043 nonn
%O A282043 1,1
%A A282043 _N. J. A. Sloane_, Feb 20 2017