A282035 Sum of quadratic residues of (n-th prime == 3 mod 4).

1, 7, 22, 76, 92, 186, 430, 423, 767, 1072, 994, 1343, 1577, 2369, 2675, 3683, 3930, 4587, 5134, 6520, 6012, 7518, 7831, 8955, 10761, 11596, 12258, 12428, 14809, 15517, 16802, 19527, 23025, 21148, 26811, 29148, 28720, 31929, 35247, 33321, 41900, 41807, 44778, 47844, 51856, 52771, 51253, 57466

Offset: 1

Author

N. J. A. Sloane, Feb 20 2017

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Aebi, Christian, and Grant Cairns. Sums of Quadratic residues and nonresidues, arXiv preprint arXiv:1512.00896 (2015).

Crossrefs

Sums of residues, nonresidues, and their differences, for p == 1 mod 4, p == 3 mod 4, and all p: A171555; A282035, A282036, A282037; A076409, A125615, A282038.

Programs

Maple

with(numtheory):
a:=[]; m:=[]; d:=[];
for i1 from 1 to 200 do
p:=ithprime(i1);
if (p mod 4) = 3 then
sp:=0; sm:=0;
for j from 1 to p-1 do
if legendre(j,p)=1 then sp:=sp+j; else sm:=sm+j; fi; od;
a:=[op(a),sp]; m:=[op(m),sm]; d:=[op(d),sm-sp];
fi;
od:
a; m; d; # A282035, A282036, A282037

Mathematica

Table[Table[Mod[a^2, p], {a, 1, (p-1)/2}]//Total, {p, Select[Prime[Range[100]], Mod[#, 4]==3 &]}] (* Vincenzo Librandi, Feb 21 2017 *)
Table[Total[PowerMod[#,2,n]&/@Range[n/2]],{n,Select[Prime[Range[100]],Mod[#,4]==3&]}] (* Harvey P. Dale, Dec 11 2024 *)

PARI

do(p)=sum(k=1,p-1,k^2%p)/2
apply(do, select(p->p%4==3, primes(100))) \\ Charles R Greathouse IV, Feb 21 2017