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A282036 Sum of quadratic nonresidues of (n-th prime == 3 mod 4). 7
2, 14, 33, 95, 161, 279, 473, 658, 944, 1139, 1491, 1738, 1826, 2884, 2996, 4318, 4585, 5004, 6191, 6683, 7849, 8413, 10314, 10746, 11394, 13157, 13393, 16013, 16566, 18936, 19783, 20376, 23946, 27057, 27804, 30883, 35541, 35232, 36384, 39832, 45671, 50858, 51363, 50059, 55097, 56040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Christian Aebi, Grant Cairns, Sums of Quadratic residues and nonresidues, 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

# Alternative:

f:= p -> convert({$1..p-1} minus {seq(k^2 mod p, k=1..(p-1)/2)}, `+`):

map(f, select(isprime, [seq(p, p=3..1000, 4)])); # Robert Israel, Mar 28 2017

MATHEMATICA

f[p_] := Total[Range[p-1] ~Complement~ Table[Mod[k^2, p], {k, (p-1)/2}] ]; f /@ Select[Range[3, 1000, 4], PrimeQ] (* Jean-Fran├žois Alcover, Feb 16 2018, after Robert Israel *)

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: A231050 A322074 A083015 * A050591 A073535 A225292

Adjacent sequences:  A282033 A282034 A282035 * A282037 A282038 A282039

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved

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Last modified May 30 15:43 EDT 2020. Contains 334726 sequences. (Running on oeis4.)