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A282725 Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p that are > p/2. 1
2, 31, 82, 379, 815, 892, 1520, 2441, 3840, 4005, 5104, 6858, 8928, 10740, 13507, 15795, 18516, 21453, 24225, 27975, 36584, 38901, 44044, 49499, 48060, 53771, 57606, 64358, 63845, 68569, 74783, 79290, 88512, 90711, 92810, 105908, 119870, 128797, 133819, 144151, 148620, 156741, 172650, 191105 (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:=[]; 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

MATHEMATICA

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

sum /@ Select[Range[3, 1000, 8], PrimeQ] (* Jean-Fran├žois Alcover, Aug 31 2018 *)

CROSSREFS

Cf. A282035-A282043 and A282721-A282727.

Sequence in context: A175446 A054207 A104095 * A030459 A141978 A212569

Adjacent sequences:  A282722 A282723 A282724 * A282726 A282727 A282728

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)