The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A282723 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A282723

Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic residues mod p.
(history; published version)

#12 by R. J. Mathar at Fri Apr 07 12:58:22 EDT 2017

STATUS

editing

approved

#11 by R. J. Mathar at Fri Apr 07 12:58:16 EDT 2017

REFERENCES

Aebi, Christian, and Grant Cairns. "Sums of Quadratic residues and nonresidues." arXiv preprint arXiv:1512.00896 (2015).

LINKS

Aebi, Christian, and Grant Cairns. <a href="http://arxiv.org/abs/1512.00896">Sums of Quadratic residues and nonresidues</a>, arXiv preprint arXiv:1512.00896 (2015).

STATUS

approved

editing

#10 by Bruno Berselli at Tue Feb 21 08:16:13 EST 2017

STATUS

proposed

approved

#9 by Vincenzo Librandi at Tue Feb 21 08:06:21 EST 2017

STATUS

editing

proposed

Discussion

Tue Feb 21

08:16

Bruno Berselli: Stop here for today, Vincenzo. Thanks.

#8 by Vincenzo Librandi at Tue Feb 21 08:06:06 EST 2017

COMMENTS

Needs a b-file

LINKS

Vincenzo Librandi, <a href="/A282723/b282723.txt">Table of n, a(n) for n = 1..2500</a>

MATHEMATICA

Table[Table[Mod[a^2, p], {a, 1, (p-1)/2}]//Total, {p, Select[Prime[Range[100]], Mod[#, 8] == 3 &]}] (* Vincenzo Librandi, Feb 21 2017 *)

STATUS

approved

editing

#7 by N. J. A. Sloane at Mon Feb 20 22:24:10 EST 2017

MAPLE

Ql; Qu; Q; Nl; Nu; N; Th; # A282721 - A282727

Discussion

Mon Feb 20

22:24

OEIS Server: https://oeis.org/edit/global/2604

#6 by N. J. A. Sloane at Mon Feb 20 22:20:02 EST 2017

CROSSREFS

Cf. A282035-A282xxxA282043 and A282721-A282727.

Discussion

Mon Feb 20

22:20

OEIS Server: https://oeis.org/edit/global/2603

#5 by N. J. A. Sloane at Mon Feb 20 22:06:16 EST 2017

STATUS

editing

approved

#4 by N. J. A. Sloane at Mon Feb 20 22:06:14 EST 2017

NAME

qqq

Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic residues mod p.

COMMENTS

Needs a b-file

REFERENCES

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

CROSSREFS

Cf. A282035-A282xxx.

STATUS

approved

editing

#3 by N. J. A. Sloane at Mon Feb 20 22:05:34 EST 2017

STATUS

editing

approved