login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282037 Let p = n-th prime == 3 mod 4; a(n) = (sum of quadratic nonresidues mod p) - (sum of quadratic residues mod p). 7
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 13:37 EDT 2021. Contains 343153 sequences. (Running on oeis4.)