[seqfan] Re: New sequence?

[Claudio Meller]

I First make thevsequence un spanish, but I send the english versión to the
Oeis

Claudio Meller
http://grageasdefarmacia.blogspot.com
http://todoanagramas.blogspot.com/
http://simplementenumeros.blogspot.com/


El El vie, 5 jul 2024 a la(s) 21:48, M. F. Hasler <oeis at hasler.fr> escribió:

> 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)."
> >
>
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