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A060395
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Smallest prime that divides k^2 + k + n for k = 0, 1, 2, ....
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2
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2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 11, 2, 3, 2, 3, 2, 17, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 41, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 11
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n)=2 if n is equal to 0, 2 or 4 modulo 6; a(n)=3 if n is equal to 1 or 3 modulo 6.
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EXAMPLE
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To obtain a(7), note that x^2+x+7 takes the values 7,9,13,19,... for k=0,1,2,... and the smallest prime dividing these numbers is 3.
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MATHEMATICA
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a[n_] := Switch[n, 0, 2, 1, 3, _, Module[{f, kmax0 = 2}, f[kmax_] := f[kmax] = MinimalBy[Table[{k, FactorInteger[k^2 + k + n][[1, 1]]}, {k, 0, kmax}], Last, 1]; f[kmax = kmax0]; f[kmax = 2 kmax]; While[f[kmax] != f[kmax/2], kmax = 2 kmax]; f[kmax][[1, 2]]]];
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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