A282039 -id:A282039 - cp's OEIS frontend

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

N. J. A. Sloane, Feb 20 2017

nonn

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

Cf. A282035-A282042 and A282721-A282727.

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 jA282039, A282040, A282041, A282039 again, A282042, A282043

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

A282040 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p that are > p/2.

Original entry on oeis.org

4, 59, 126, 285, 679, 953, 1706, 2675, 3709, 4269, 5551, 6480, 8488, 8858, 11194, 12212, 15103, 20665, 23511, 24153, 30197, 32733, 38458, 36913, 42643, 42032, 59638, 64987, 70396, 70887, 85606, 94192, 95522, 99930, 123090, 117932, 130367, 134436, 141262, 149395, 169769, 167663, 175469

Offset: 1

N. J. A. Sloane, Feb 20 2017

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Christian Aebi and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 [math.NT], 2015.

Cf. A282035-A282043 and A282721-A282727.

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 jA282039, A282040, A282041, A282039 again, A282042, A282043
# alternative:
g:= proc(t, p) if t > p/2 then t else 0 fi end proc;
f:= proc(n) local k;
     add(g(k^2 mod n, n), k=1..n/2)
end proc:
P:= select(isprime, [seq(i, i=7..3000, 8)]):
map(f, P); # Robert Israel, Aug 22 2025

sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] == 1, #, 0]& /@ Range[p-1]];
sum /@ Select[Range[7, 1000, 8], PrimeQ] (* Jean-François Alcover, Aug 31 2018 *)

A282041 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p.

Original entry on oeis.org

7, 92, 186, 423, 994, 1343, 2369, 3683, 5134, 6012, 7831, 8955, 11596, 12428, 15517, 16802, 21148, 28720, 31929, 33321, 41807, 44778, 51856, 51253, 57466, 57845, 82063, 88015, 95281, 97050, 117916, 127225, 130025, 135180, 165423, 161927, 176915, 183609, 193132, 202180, 228212, 228056, 236849

Offset: 1

N. J. A. Sloane, Feb 20 2017

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..2500
Aebi, Christian, and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 (2015).

Cf. A282035-A282043 and A282721-A282727.

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 jA282039, A282040, A282041, A282039 again, A282042, A282043

Table[Table[Mod[a^2, p], {a, 1, (p-1)/2}]//Total, {p, Select[Prime[Range[100]], Mod[#, 8] == 7 &]}] (* Vincenzo Librandi, Feb 21 2017 *)

A282042 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2.

Original entry on oeis.org

11, 128, 219, 520, 1176, 1348, 2221, 3310, 4766, 6106, 8034, 8271, 10049, 12443, 14613, 15193, 21012, 27486, 26814, 30664, 39248, 39318, 41699, 48888, 46052, 52595, 74613, 72878, 78599, 85768, 107895, 103643, 111125, 111195, 130497, 145619, 148490, 160159, 169503, 166856, 180406, 194204

Offset: 1

N. J. A. Sloane, Feb 20 2017

nonn

Robert Israel, Table of n, a(n) for n = 1..1000
Aebi, Christian, and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 (2015).

Cf. A282035-A282043 and A282721-A282727.

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 jA282039, A282040, A282041, A282039 again, A282042, A282043

sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] != 1, #, 0]& /@ Range[p-1]];
sum /@ Select[Range[7, 1000, 8], PrimeQ] (* Jean-François Alcover, Aug 31 2018 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A282040 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p that are > p/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A282041 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A282042 Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica