OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..4000
Christian Aebi and Grant Cairns, Sums of Quadratic residues and nonresidues, arXiv:1512.00896 [math.NT], 2015.
MAPLE
with(numtheory):
Ql:=[]; Qu:=[]; Q:=[]; Nl:=[]; Nu:=[]; N:=[]; Th:=[];
for i1 from 1 to 300 do
p:=ithprime(i1);
if (p mod 8) = 3 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];
Th:=[op(Th), q+ql];
fi;
od:
# Alternative
f:= proc(p) local q, r, t, j;
r:= (p-1)/2; t:= 0;
for j from 1 to r do
q:= j^2 mod p;
if q <= r then t:= t+q fi;
od:
t
end proc:
map(f, select(isprime, [seq(i, i=3..10000, 8)])); # Robert Israel, Mar 27 2017
MATHEMATICA
s[p_] := Total[Select[Range[Floor[p/2]], JacobiSymbol[#, p] == 1&]];
s /@ Select[Range[3, 2000, 8], PrimeQ] (* Jean-François Alcover, Nov 17 2017 *)
PROG
(Python)
from sympy import isprime
def a(p):
r=(p - 1)//2
t=0
for j in range(1, r + 1):
q=(j**2)%p
if q<=r:t+=q
return t
print([a(p) for p in range(3, 2001, 8) if isprime(p)]) # Indranil Ghosh, Mar 27 2017, translated from Maple code
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 20 2017
STATUS
approved