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A282038
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(Sum of the quadratic nonresidues of prime(n)) - (sum of the quadratic residues of prime(n)).
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7
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-1, 1, 0, 7, 11, 0, 0, 19, 69, 0, 93, 0, 0, 43, 235, 0, 177, 0, 67, 497, 0, 395, 249, 0, 0, 0, 515, 321, 0, 0, 635, 655, 0, 417, 0, 1057, 0, 163, 1837, 0, 895, 0, 2483, 0, 0, 1791, 633, 1561, 1135, 0, 0, 3585, 0, 1757, 0, 3419, 0, 2981, 0, 0, 849, 0, 921, 5909, 0, 0, 993, 0, 1735, 0, 0, 6821, 3303, 0
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OFFSET
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1,4
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COMMENTS
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Equals 0 if p == 1 (mod 4).
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LINKS
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MAPLE
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with(numtheory):
a:=[]; m:=[]; d:=[];
for i1 from 1 to 100 do
p:=ithprime(i1);
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];
od:
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MATHEMATICA
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sum[p_] := Total[If[JacobiSymbol[#, p] == 1, -#, #]& /@ Range[p-1]];
a[n_] := sum[Prime[n]];
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PROG
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(PARI) a(n) = my (p=prime(n)); return (sum(i=1, p-1, if (kronecker(i, p)==1, -i, +i))) \\ Rémy Sigrist, Apr 28 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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