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A241604
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Least Fibonacci number smaller than prime(n)/2 which is a quadratic nonresidue modulo prime(n), or 0 if such a Fibonacci number does not exist.
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5
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0, 0, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 2, 2, 2, 13, 5, 3, 2, 3, 5, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 21, 5, 2, 3, 2, 3, 2, 2, 3, 13, 13, 2, 3, 5, 2, 3, 2, 3, 2, 2, 2, 34, 5, 2, 2, 5, 2, 2, 3, 13, 3, 2, 2, 5, 2, 2, 3, 13
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OFFSET
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1,3
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COMMENTS
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According to the conjecture in A241568, a(n) should be positive for all n > 2.
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LINKS
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EXAMPLE
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a(4) = 3 since the Fibonacci number F(4) = 3 < prime(4)/2 is a quadratic nonresidue modulo prime(4) = 7, but the Fibonacci numbers F(1) = F(2) = 1 and F(3) = 2 are quadratic residues modulo prime(4) = 7.
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MATHEMATICA
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f[k_]:=Fibonacci[k]
Do[Do[If[f[k]>Prime[n]/2, Goto[bb]]; If[JacobiSymbol[f[k], Prime[n]]==-1, Print[n, " ", Fibonacci[k]]; Goto[aa]]; Continue, {k, 1, (Prime[n]+1)/2}]; Label[bb]; Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 80}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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