[seqfan] Re: Atomic number of n-th element in the "neptunium series"

[M. F. Hasler]

FWIW, my personal 2 cents:

> Atomic number of n-th element in the "neptunium series"
> https://en.wikipedia.org/wiki/Decay_chain#Neptunium_series
> The sequence starts 93, 91, 92, 90, 88, 89, 87, 85, 83, 0, 82, 83, 81
> (...) I don't know if this sequence is interesting.

although I'm generally against non-mathematical and "weakly defined" sequences,
I think this one can be considered as quite interesting and reasonably
scientific & well defined, even if it has to be truncated slightly
arbitrarily at both ends.

>> The "0" term may be a bit unsatisfactory, but I am not sure of a better way to resolve the issue
> If this is added, I think each term should be the atomic number of the most common element at that step.

I think this is a very good proposal from Frank

>> Maybe, rather than counting down, it should be increasing, with a(1) = the
>> the final stable decay product? That way, any "trans-neptunian" elements
>> discovered in the future would simply extend the sequence.
>
> Ah, but what counts as "stable"? (...)

I'm rather in favour of the decreasing version, because this is far
more natural, given the nature of the process.
This does not limit the possibility of extending the sequence to the left:
The offset does not matter for search purposes. It can be chosen in
any way we may consider reasonable.
For example, assign offset 0 to the first element which has half-life
>= 10^10 years, the age of the universe,
and give negative indices to the preceding elements.

> (...) there are four classes of radioactive nuclei. The Np-237 series
> all have mass number of the form 4n+1. It is called the Neptunium series
> (...) Four prior members are now known: Californium-249, Curium-245,
> Plutonium-241, and Americium-241 (which decays into Neptunium-237).
> The 4n series's earliest known member is Californium-252 and is called the
> Thorium series; 4n+2 starts with Uranium-238 and is named after it; and
> 4n+3 starts with Californium-251 and is called the Actinium series.

I think we could add all four of these.

- Maximilian