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A107784
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Stable nuclear atomic numbers based on an semi-empirical formula.
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0
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2, 6, 7, 17, 18, 19, 20, 21, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156
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refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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This function was derived as an expansion of : n/Log(n],n/(log[n]-1) in terms of n ( PrimePi[n] like) . I noticed that it was giving ionization potential like output and adjusted it to give those values where the function was better than average. It corresponded to stable nuclear atomic numbers. It predicts a stability plateau around atomic number 146.
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LINKS
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FORMULA
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f(n)=n*Sum[m/Product[ -Log[n] + (k - 1), {k, 1, m}], {m, 1, Infinity}] a(n) = if Floor[n*Abs[Re[f[n]]]/(n - 1)]>average then Floor[n*Abs[Re[f[n]]]/(n - 1)]
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MATHEMATICA
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f[n_] = n*Sum[m/Product[ -Log[n] + (k - 1), {k, 1, m}], {m, 1, Infinity}] a0 = Table[Floor[n*Abs[Re[f[n]]]/(n - 1)], {n, 2, 250}] a00 = Apply[Plus, a0]/Length[a0] b0 = Flatten[Table[If[a0[[n]] > a00, n, {}], {n, 1, Length[a0]}]]
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CROSSREFS
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KEYWORD
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nonn,uned,obsc,less
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AUTHOR
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STATUS
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approved
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