cp's OEIS Frontend

A282726 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p .

%I A282726 #13 Nov 05 2020 13:48:05
%S A282726 2,33,95,473,944,1139,1826,2996,4585,5004,6683,8413,11394,13393,16566,
%T A282726 20376,23946,27804,30883,36384,45671,50059,56040,62357,62874,69559,
%U A282726 75486,81635,82795,88050,97183,104166,112030,118159,120925,138193,156613,167066,173670,187262,196026,206796,226333,242750
%N A282726 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p .
%H A282726 Vincenzo Librandi, <a href="/A282726/b282726.txt">Table of n, a(n) for n = 1..2500</a>
%H A282726 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 A282726 with(numtheory):
%p A282726 Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[]; Th:=[];
%p A282726 for i1 from 1 to 300 do
%p A282726 p:=ithprime(i1);
%p A282726 if (p mod 8) = 3 then
%p A282726 ql:=0; qu:=0; q:=0; nl:=0; nu:=0; n:=0;
%p A282726 for j from 1 to p-1 do
%p A282726 if legendre(j,p)=1 then
%p A282726 q:=q+j;
%p A282726 if j<p/2 then ql:=ql+j; else qu:=qu+j; fi;
%p A282726 else
%p A282726 n:=n+j;
%p A282726 if j<p/2 then nl:=nl+j; else nu:=nu+j; fi;
%p A282726 fi;
%p A282726 od;
%p A282726 Ql:=[op(Ql),ql];
%p A282726 Qu:=[op(Qu),qu];
%p A282726 Q:=[op(Q),q];
%p A282726 Nl:=[op(Nl),nl];
%p A282726 Nu:=[op(Nu),nu];
%p A282726 N:=[op(N),n];
%p A282726 Th:=[op(Th),q+ql];
%p A282726 fi;
%p A282726 od:
%p A282726 Ql; Qu; Q; Nl; Nu; N; Th; # A282721 - A282727
%t A282726 Table[Table[Mod[a^2, p/2], {a, 1, (p-1)}]//Total, {p, Select[Prime[ Range[ 200]], Mod[#, 8] == 3 &]}] (* _Vincenzo Librandi_, Feb 22 2017 *)
%Y A282726 Cf. A282035-A282043 and A282721-A282727.
%K A282726 nonn
%O A282726 1,1
%A A282726 _N. J. A. Sloane_, Feb 20 2017