A282042 - OEIS

A282042

Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2.

11, 128, 219, 520, 1176, 1348, 2221, 3310, 4766, 6106, 8034, 8271, 10049, 12443, 14613, 15193, 21012, 27486, 26814, 30664, 39248, 39318, 41699, 48888, 46052, 52595, 74613, 72878, 78599, 85768, 107895, 103643, 111125, 111195, 130497, 145619, 148490, 160159, 169503, 166856, 180406, 194204

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Robert Israel, 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:=[];

for i1 from 1 to 300 do

p:=ithprime(i1);

if (p mod 8) = 7 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];

fi;

od:

Ql; Qu; Q; Nl; Nu; N; # A282039, A282040, A282041, A282039 again, A282042, A282043

MATHEMATICA

sum[p_]:= Total[If[#>p/2 && JacobiSymbol[#, p] != 1, #, 0]& /@ Range[p-1]];

sum /@ Select[Range[7, 1000, 8], PrimeQ] (* Jean-François Alcover, Aug 31 2018 *)

CROSSREFS

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A363111 A181012 A168327 * A015601 A024144 A201877

Adjacent sequences: A282039 A282040 A282041 * A282043 A282044 A282045

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved