A282037 - OEIS

A282037

Let p = n-th prime == 3 mod 4; a(n) = (sum of quadratic nonresidues mod p) - (sum of quadratic residues mod p).

1, 7, 11, 19, 69, 93, 43, 235, 177, 67, 497, 395, 249, 515, 321, 635, 655, 417, 1057, 163, 1837, 895, 2483, 1791, 633, 1561, 1135, 3585, 1757, 3419, 2981, 849, 921, 5909, 993, 1735, 6821, 3303, 1137, 6511, 3771, 9051, 6585, 2215, 3241, 3269, 11975, 3409, 4419, 1497, 10563, 2615, 1641, 5067, 2855

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OFFSET

1,2

COMMENTS

Equals A282036 - A282035.

LINKS

Rémy Sigrist, 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).

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

sum[p_] := Total[If[JacobiSymbol[#, p] == 1, -#, #]& /@ Range[p-1]];

sum /@ Select[Prime[Range[200]], Mod[#, 4] == 3&] (* Jean-François Alcover, Aug 31 2018 *)

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.

Sequence in context: A323109 A023267 A319224 * A050562 A321806 A057190

Adjacent sequences: A282034 A282035 A282036 * A282038 A282039 A282040

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved