[seqfan] Re: A026081 Integers in reverse alphabetical order in U.S. English.

[Michael Porter]

I intend to submit the following changes to A026081 (please see comments after list):

1. Change name to "Integers less than 10^66 in reverse alphabetical order in U.S. English."

2. Change terms beyond initial zero to those listed by Andrew Weimholt below.

3. Change example to:
zero,
two vigintillion two undecillion two trillion two thousand two hundred two,
two vigintillion two undecillion two trillion two thousand two hundred
twenty two, etc.

4. Add cross-references to sequences A060365 and A060366.

5. Add the following links:
http://mathworld.wolfram.com/LargeNumber.html
http://en.wikipedia.org/wiki/Names_of_large_numbers
http://www.isthe.com/chongo/tech/math/number/howhigh.html
http://www.mrob.com/pub/math/largenum.html
http://www.quadibloc.com/math/bignum.htm

6. Add the following comments:
This sequence used to be named "Integers in reverse alphabetical order
in U.S. English."

Since the use of alphabetic names is rare for numbers greater than 10^15, there is no universal agreement on the naming scheme for large integers, and there is some question whether this sequence would well-defined without the "less than 10^66" clause.

The Wikipedia article compares 8 dictionary sources and has names for the powers of 1000 up to 10^63 and for 10^303.  These are also in the Mathworld link.

There are several conflicting schemes for extending the dictionary definitions.  If we assume that the system of alphabetic names greater than 10^63 defines a word for every power of 1000 and that word comes before "vigintillion" alphabetically, the sequence can include all integers.  However, many of the extension schemes listed do not meet that standard - some have multiple words and some have words that are alphabetically after "vigintillion".  Therefore, the definition of the sequence has been changed so that it will depend only on the dictionary words.

The terms are from Andrew Weimholt (andrew(AT)weimholt.com)

(END)

I think that explains the situation accurately, preserves the sequence, and answers Maximilian's objection that the sequence is not well-defined.  I think his objection is dependent on his particular idea of what should happen after 10^63, but the addition of the "less than 10^66" clause makes it a moot point.

I will leave the "dumb" keyword in, though I think it may not be warranted in this case.  Remember that I believe that it has to be really, really dumb to earn the "dumb" keyword.

I found two additional sequences, A060365 and A060366, which also deal with names for large numbers.  There is also a file associated with these sequences that lists names for powers of 1000 beyond 10^63:
http://www.research.att.com/~njas/sequences/a060365.txt

I would welcome additional references or ideas for comments.

Thank you,
Michael Porter



--- On Wed, 11/18/09, Andrew Weimholt <andrew.weimholt at gmail.com> wrote:

From: Andrew Weimholt <andrew.weimholt at gmail.com>
Subject: [seqfan] Re: A026081 Integers in reverse alphabetical order in U.S. English.
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Date: Wednesday, November 18, 2009, 12:28 AM

On 11/17/09, Michael Porter <ic_designer at verizon.net> wrote:
>
>  Do we have a procedure for sequences that are wrong but we don't have the correct values?  If not, could someone who knows what they're doing please fix it?  Barring that, if the choice is really between deleting it and fixing it, I guess I could take my best shot at fixing it.
>

Here are the correct names, and values...

two vigintillion two undecillion two trillion two thousand two hundred two
two vigintillion two undecillion two trillion two thousand two hundred
twenty two
two vigintillion two undecillion two trillion two thousand two hundred
twenty three
two vigintillion two undecillion two trillion two thousand two hundred
twenty six
two vigintillion two undecillion two trillion two thousand two hundred
twenty seven
two vigintillion two undecillion two trillion two thousand two hundred
twenty one
two vigintillion two undecillion two trillion two thousand two hundred
twenty nine
two vigintillion two undecillion two trillion two thousand two hundred
twenty four
two vigintillion two undecillion two trillion two thousand two hundred
twenty five
two vigintillion two undecillion two trillion two thousand two hundred
twenty eight
two vigintillion two undecillion two trillion two thousand two hundred twenty
two vigintillion two undecillion two trillion two thousand two hundred twelve
two vigintillion two undecillion two trillion two thousand two hundred three
two vigintillion two undecillion two trillion two thousand two hundred
thirty two
two vigintillion two undecillion two trillion two thousand two hundred
thirty three

2000000000000000000000000002000000000000000000000002000000002202,
2000000000000000000000000002000000000000000000000002000000002222,
2000000000000000000000000002000000000000000000000002000000002223,
2000000000000000000000000002000000000000000000000002000000002226,
2000000000000000000000000002000000000000000000000002000000002227,
2000000000000000000000000002000000000000000000000002000000002221,
2000000000000000000000000002000000000000000000000002000000002229,
2000000000000000000000000002000000000000000000000002000000002224,
2000000000000000000000000002000000000000000000000002000000002225,
2000000000000000000000000002000000000000000000000002000000002228,
2000000000000000000000000002000000000000000000000002000000002220,
2000000000000000000000000002000000000000000000000002000000002212,
2000000000000000000000000002000000000000000000000002000000002232,
2000000000000000000000000002000000000000000000000002000000002233

see also...
http://isthe.com/chongo/tech/math/number/tenpower.html

Andrew


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