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

14, 161, 279, 658, 1491, 1738, 2884, 4318, 6191, 7849, 10314, 10746, 13157, 16013, 18936, 19783, 27057, 35541, 35232, 39832, 50858, 51363, 55097, 63228, 60875, 68408, 97038, 95906, 103484, 111931, 140205, 136676, 145628, 146445, 172830, 189614, 195038, 209332, 221373, 219641, 238849, 254597

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Aebi, Christian, and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 (2015).

Maple

with(numtheory):
Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[];
for i1 from 1 to 300 do
p:=ithprime(i1);
if (p mod 8) = 7 then
ql:=0; qu:=0; q:=0; nl:=0; nu:=0; n:=0;
for j from 1 to p-1 do
if legendre(j, p)=1 then
q:=q+j;
if j<p/2 then ql:=ql+j; else qu:=qu+j; fi;
else
n:=n+j;
if j<p/2 then nl:=nl+j; else nu:=nu+j; fi;
fi;
od;
Ql:=[op(Ql), ql];
Qu:=[op(Qu), qu];
Q:=[op(Q), q];
Nl:=[op(Nl), nl];
Nu:=[op(Nu), nu];
N:=[op(N), n];
fi;
od:
Ql; Qu; Q; Nl; Nu; N; # A282039, A282040, A282041, A282039 again, A282042, A282043

Mathematica

sqnr[p_] := Select[Range[p-1], JacobiSymbol[#, p] != 1&] // Total;
sqnr /@ Select[Prime[Range[200]], Mod[#, 8] == 7&] (* Jean-François Alcover, Aug 30 2018 *)

Crossrefs

Cf. A282035-A282042 and A282721-A282727.

Sequence in context: A268946 A343093 A229611 * A193103 A016206 A161158

Adjacent sequences: A282040 A282041 A282042 * A282044 A282045 A282046

Keyword

nonn

Author

N. J. A. Sloane, Feb 20 2017

Status

approved