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A282724 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p that are < p/2. 2
0, 2, 13, 94, 129, 247, 306, 555, 745, 999, 1579, 1555, 2466, 2653, 3059, 4581, 5430, 6351, 6658, 8409, 9087, 11158, 11996, 12858, 14814, 15788, 17880, 17277, 18950, 19481, 22400, 24876, 23518, 27448, 28115, 32285, 36743, 38269, 39851, 43111, 47406, 50055, 53683, 51645, 58274, 66410, 65119, 76013, 80465 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jean-François Alcover, 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).

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

A282724 := proc(n)

    local p, a, r;

    p := A007520(n) ;

    a := 0 ;

    for r from 1 to (p-1)/2 do

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

            a := a+r ;

        end if;

    end do:

    a ;

end proc:

seq(A282724(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 = 1, r <= (p - 1)/2, r++, If[KroneckerSymbol[r, p] != 1, q = q + r]]; q];

Array[a, 50] (* Jean-François Alcover, Nov 27 2017, after R. J. Mathar *)

CROSSREFS

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A300764 A209470 A140636 * A104255 A118352 A320360

Adjacent sequences:  A282721 A282722 A282723 * A282725 A282726 A282727

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved

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Last modified June 16 14:16 EDT 2021. Contains 345057 sequences. (Running on oeis4.)