[seqfan] Re: New sequence?

[M. F. Hasler]

On Wed, Jul 3, 2024 at 11:35 AM Neil Sloane <njasloane at gmail.com> wrote:

> Hans, In that case I will withdraw my objection. Sequences with an
> interesting history are usually welcome.
> Can you please create an OEIS entry for it?
>

And what about other languages?
I've written a function A340671(n,cf=English)
that takes the sorting key function as an optional argument,
initially to get also the "ignore spaces and hyphens" variant
(with cf = x-> [c | c<-Vec(English(x)), c>"@"])
but we can also use other languages as sort key:

For German (cf. A007208) I get
[A340671(n,German)|n<-[1..99]]
= [1, 2, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 3, 1,
2, 2, 2, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0,
0, 0, 0, 0, 0, 4, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0,
1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 3, 2, 3, 1, 1]

For example, a(12)=3 because:

sort(n, key=English, f)=vecsort([1..n], x->key(x), 1)
sort(12, German)
= Vecsmall([8, 3, 1, 11, 5, 9, 6, 7, 4, 10, 2, 12])
apply(German,Vec(%))
= ["acht", "drei", "eins", "elf", "fünf", "neun", "sechs", "sieben",
"vier", "zehn", "zwei", "zwölf"]

We see that 5 = fünf, 10 = zehn  & 12 = zwölf  are in their
original position.

For French (cf. A167507) I get:

[A340671(n,French)|n<-[1..99]]
=[1, 0, 0, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 5, 6, 7, 6,
6, 6, 7, 5, 6, 3, 3, 4, 5, 3, 3, 3, 3, 3, 3, 3, 5, 4, 3, 3, 4, 3, 3, 3, 5,
2, 3, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0]

sort(23, French)
= Vecsmall([5, 2, 10, 18, 19, 17, 12, 8, 9, 11, 14, 4, 15, 16, 7, 6, 13, 3,
1, 20, 21, 22, 23])
apply(French, Vec(%))
= ["cinq", "deux", "dix", "dix-huit", "dix-neuf", "dix-sept", "douze",
"huit", "neuf", "onze", "quatorze", "quatre", "quinze", "seize", "sept",
"six", "treize", "trois", "un", "vingt", "vingt et un", "vingt-deux",
"vingt-trois"]

Here, my function "French" uses the traditional style with space and not
hyphen when there is "xxx et un".
Therefore the last 4 terms in the above list are "at their place".
In the "reformed style" it would read "vingt-et-un" and then be sorted
after  "vingt-deux",
which would yield two fixed points less.
In view of that it might be a good idea to ignore spaces and hyphens for
French,
or, use always "-" (reformed orthography), i.e., consider " " and "-" as
equivalent.

Similar ambivalence as with the word "and" in English
(e.g., "one hundred one" vs "one hundred and one").

- Maximilian


> On Tue, Jul 2, 2024 at 2:44 PM Hans Havermann <gladhobo at bell.net> wrote:
> > Notwithstanding, Claudio's proposed sequence has an interesting history.
> > In 1981, A. Ross Eckler wrote an article in Word Ways called
> "Alphabetizing
> > the Integers" (Vol. 14, #1, pages 18-20):
> >
> >
> https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=2556&context=wordways
> >
> > Eckler quotes Howard Bergerson: "I have had one research problem in mind
> > for a long time -- I once did some preliminary work on it -- which could
> > turn out to be any­thing from easy to formidable to practically
> impossible.
> > It is this: Imagine the one thousand vigintillion minus one (if you don't
> > in­clude zero) consecutively named numbers arranged in alphabetical order
> > and also in numerical order. How many (if any) numbers have their
> positions
> > the same in both lists? What is the least such number? ... Does this
> > intrigue you enough to have a shot at it?"
> >
> > Eckler has a shot at it, noting on page 20 that "Philip Cohen has pointed
> > out that Bergerson's problem can be re­garded as one member of a class of
> > matching problems: the integers 1 through n can be alphabetized, where n
> > takes on any integral value." This is followed by nine lists of
> > small-integer names with underlines corresponding to Claudio's [[1], [1,
> > 2], [1], [3], 0, 0, 0, [6], 0, ...].
> >
> > Mathematica has progressed from its once-largest IntegerName[10^66-1] to
> > IntegerName[10^306-1] so, while perhaps not yet canonical, the problem
> > could be restated using the much larger number range.
> >
> > Eckler notes an alphabetization-interpretation issue at the end but
> > clearly states a preference for his article that "the space is assumed to
> > precede the letter A in alphabetization (e.g., eight hundred before
> > eighteen)."
>