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A306220
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a(n) is the smallest prime p such that Kronecker(-n,p) = -1.
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3
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3, 5, 2, 3, 2, 13, 3, 5, 7, 3, 2, 5, 2, 11, 7, 3, 5, 5, 2, 11, 2, 3, 5, 13, 3, 11, 2, 3, 2, 7, 3, 5, 5, 3, 2, 7, 2, 5, 7, 3, 13, 5, 2, 7, 2, 3, 5, 5, 3, 7, 2, 3, 2, 13, 3, 11, 5, 3, 2, 7, 2, 5, 5, 3, 7, 19, 2, 5, 2, 3, 7, 5, 3, 7, 2, 3, 2, 5, 3, 11, 7, 3, 2, 13, 2, 7, 5
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OFFSET
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1,1
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COMMENTS
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Conjecture: lim sup log(a(n))/log(n) = 0. For example, it seems that log(a(n))/log(n) < 0.5 for all n > 1364.
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LINKS
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FORMULA
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a(n) = 2 if and only if n == 3, 5 (mod 8). See A047621.
a(n) = 3 if and only if n == 1, 4, 7, 10, 16, 22 (mod 24).
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MAPLE
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# This requires Maple 2016 or later
f:= proc(n) local p;
p:= 2;
while NumberTheory:-KroneckerSymbol(-n, p) <> -1 do p:= nextprime(p) od:
p
end proc:
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MATHEMATICA
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a[n_] := For[p = 2, True, p = NextPrime[p], If[KroneckerSymbol[-n, p] == -1, Return[p]]];
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PROG
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(PARI) a(n) = forprime(p=2, , if(kronecker(-n, p)<0, return(p)))
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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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