[seqfan] Re: An error in a silly sequence

David Wilson davidwwilson at comcast.net
Fri Apr 10 09:44:51 CEST 2009

I agree with MH that this is a "lazy sequence". When I first started working
on the OIES (back in the A02**** days), I used to enjoy fixing up new
sequences that were submitted. But since then, the flood of poor-quality
sequences has grown to the point that the corrective task is overwhelming.
For my part, I have adopted the policy of never submitting a sequence
before its time, and I am sitting on several probably OEISworthy sequences
that I have not submitted because I have not been able to find the 
to bring them up to my personal standards.

I also agree with MH that word-based sequences, especially those dealing
with natural languages, are often ambiguous or ill-defined. I do not agree
that this sequence is one of them, and attempting to tack it down leads us
into some interesting territory with a perhaps interesting conclusion.

Regarding the "vowelty" of a letter, most English letters are categorically
vowel or consonants, the exceptions being W and Y, which are called
semivowels not because they act as a vowel or consonant according to
context. In isolation, you cannot say whether W or Y is a vowel, but in
context you can. In the word "cow", W is a vowel, in "wait" it is a
consonant. Similarly, Y is a vowel in "say" and a consonant in "yes".

Regarding the English names of numbers, there are three major naming
systems worth mentioning, the Chuquet (10^9 = thousand million), the
Modified Chuquet(10^9 = milliard) and the American (10^9 = billion). Each
of these systems shares a complete sequence of zillion names up to a
vigintillion, which equals 10^120 in the Chuquet systems and 10^63 in
the American system. The smallest unnamable number is 10^126 in the
Chuquet systems and 10^66 in the American. All three systems have
variations in which the word "and" is permitted in or excluded from
number names.

In all three naming systems, we make the following observations:

- W never appears at the end of a number name, and whenever Y does,
it is a vowel.

- Every zillion name up to vigintillion ends in N or D.

- The inclusion or exclusion of "and" in number names does not affect
  the last letter of the number name.

- Let u be the smallest unnameable number, and let 0 < n < u. Then

   - If n is a multiple of 100, its name ends in "hundred" or a zillion
     name, therefore the name of n ends in N or D.

   - If n is not a multiple of 100, its name ends with the same letter
    as the name of (n mod 100).

These facts allow us conclude that on 0 < n < u, the "vowelness" of
the last letter of n is periodic in n with period 100, regardless of the
naming system.

Conway and Guy proposed a zillion naming system that can be used
to generate zillion names ad infinitum, and can be used to extend any
of the above naming systems to cover all nonnegative integers. Under
the reasonable assumption that all of C&G's zillion names end in
-illion or -illiard, and therefore consonants N or D, we can extend A152592
to an infinite sequence periodic with period 100 on the positive integers.

"zero" defies the pattern by ending in a vowel, just as its numeral defies
convention by starting with the digit 0.

----- Original Message ----- 
From: "Maximilian Hasler" <maximilian.hasler at gmail.com>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Thursday, April 09, 2009 10:06 PM
Subject: [seqfan] Re: An error in a silly sequence

Anyway, submitting a sequence with  keywords "easy,more" but less than
one line of data is inconsistent and a way of saying that even the
author is not really interested in the sequence, but other people
should do what he considers as a waste of (his) time.


(IMO the present example shows again that a sequence based on words of
a natural language is inherently ill defined, EVEN IF you specify
exactly the language, the place and the date where it is used.)

On Thu, Apr 9, 2009 at 8:13 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> "Y" and "W" are sometimes called "semivowels." I even mentioned this
> in some sequence comment...
> On Thu, Apr 9, 2009 at 4:45 PM, <franktaw at netscape.net> wrote:
>> A152592 is "Consider last letter of the sequence zero, one, two, three,
>> four, five, ... . Write down 0 for a vowel, 1 for a consonant."
>> However, it has a(20) = 1; but the "y" at the end of "twenty" is a
>> vowel!
>> (Anybody remember "a, e, i, o, u, and sometimes y"?)
>> Franklin T. Adams-Watters
>> _______________________________________________
>> Seqfan Mailing list - http://list.seqfan.eu/
> _______________________________________________
> Seqfan Mailing list - http://list.seqfan.eu/


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