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A282722 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic residues mod p that are > p/2. 2
0, 9, 44, 293, 461, 758, 1022, 1799, 2530, 3171, 4778, 5068, 7662, 8470, 9993, 14097, 16674, 19467, 20755, 25701, 29042, 34471, 37506, 40661, 45066, 48541, 54324, 54224, 58135, 60351, 68593, 75432, 74014, 83881, 85900, 98518, 112000, 117443, 122241, 132125, 143322, 151299, 163180, 161975, 181191 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..1000

Christian Aebi, 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:

Ql; Qu; Q; Nl; Nu; N; Th; # A282721 - A282727

# 2nd program

A282722 := proc(n)

    local p, ar;

    p := A007520(n) ;

    a := 0 ;

    for r from (p+1)/2 to p do

        if numtheory[legendre](r, p) = 1 then

            a := a+r ;

        end if;

    end do:

    a ;

end proc:

seq(A282722(n), n=1..10) ; # R. J. Mathar, Apr 07 2017

MATHEMATICA

b[1] = 3; b[n_] := b[n] = Module[{p}, p = NextPrime[b[n - 1]]; While[Mod[p, 8] != 3, p = NextPrime[p]]; p];

a[n_] := Module[{p, q, r}, p = b[n]; q = 0; For[r = (p + 1)/2, r <= p, r++, If[KroneckerSymbol[r, p] == 1, q = q + r]]; q];

Array[a, 45] (* Jean-François Alcover, Nov 27 2017, after R. J. Mathar *)

CROSSREFS

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A228603 A297491 A104470 * A084016 A221508 A301397

Adjacent sequences:  A282719 A282720 A282721 * A282723 A282724 A282725

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved

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Last modified June 22 13:46 EDT 2021. Contains 345380 sequences. (Running on oeis4.)