A107784 Stable nuclear atomic numbers based on an semi-empirical formula.

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

Offset

0,1

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 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.

Links

Table of n, a(n) for n=0..39.

Author?, Title?

Author?, Title?

Author?, Title?

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)]

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]}]]

Crossrefs

Sequence in context: A177353 A049399 A060133 * A210619 A358578 A095036

Adjacent sequences: A107781 A107782 A107783 * A107785 A107786 A107787

Keyword

nonn,uned,obsc,less

Author

Roger L. Bagula, Jun 14 2005

Status

approved