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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| This function was derived as an expansion of : n/Log(n],n/(log[n]-1) in terms of n ( PrimePi[n] like) . I noticed thast 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
| Author?, Title?
Author?, Title?
Author?, Title?
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FORMULA
| 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
| 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
| Sequence in context: A177353 A049399 A060133 * A095036 A100901 A004791
Adjacent sequences: A107781 A107782 A107783 * A107785 A107786 A107787
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KEYWORD
| nonn,uned,obsc,less
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 14 2005
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