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May 18, 1998, 3:00:00 AM5/18/98

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All:

I'm looking for a few number-theoretical properties of 38 -- my upcoming

age. You know: the smallest number that..., the only number for

which..., etc. There is a well-known proof that there are no

uninteresting numbers. Any suggestions, or pointers to Internet

resources? Thanks!

Andrew Duncan

http://www.cs.ucsb.edu/~aduncan

May 18, 1998, 3:00:00 AM5/18/98

to Andrew M. Duncan

On Mon, 18 May 1998, Andrew M. Duncan wrote:

> I'm looking for a few number-theoretical properties of 38 -- my upcoming

> age. You know: the smallest number that..., the only number for

> which..., etc. There is a well-known proof that there are no

> uninteresting numbers. Any suggestions, or pointers to Internet

> resources? Thanks!

How about...

The first 3 squares are 1, 4, and 9, and the sum of the

1st, 4th and 9th Fibonacci number is 1 + 3 + 34 = 38.

Let P(m) denote the product of the first m primes.

Then P(1) + P(2) + P(3) = 2 + 2 * 3 + 2 * 3 * 5 = 38.

Let f(1) = 1, and let f(n) = 1 + product of f(i) for

i = 1, 2, .., n. Then f(2) = 2, f(3) = 3, f(4) = 7.

The sum of the 1st, 2nd, 3rd and 7th triangular number

is 1 + 3 + 6 + 28 = 38.

Also, f(5) - f(4) + f(3) - f(2) + f(1) = 38.

2^(0^2 + 1) + 2^(1^2 + 1) + 2^(2^2 + 1) = 2 + 4 + 32 = 38.

May 18, 1998, 3:00:00 AM5/18/98

to Andrew M. Duncan

On Mon, 18 May 1998, Jan Kristian Haugland wrote:

> Let f(1) = 1, and let f(n) = 1 + product of f(i) for

> i = 1, 2, .., n. Then f(2) = 2, f(3) = 3, f(4) = 7.

^^^

Correction: i = 1, 2, ..., n - 1.

May 18, 1998, 3:00:00 AM5/18/98

to Andrew M. Duncan

On Mon, 18 May 1998, Andrew M. Duncan wrote:

> I'm looking for a few number-theoretical properties of 38 -- my upcoming

> age. You know: the smallest number that..., the only number for

> which..., etc. There is a well-known proof that there are no

> uninteresting numbers. Any suggestions, or pointers to Internet

> resources? Thanks!

Two more...

The sum of the squares of the first three primes is 4 + 9 + 25 = 38.

38 is THE ONLY positive integer n with the property that all

digits from 0 to 9 appear among the first 10 decimals after

comma in 1 / n :

1 / 38 = 0.0263157894...

May 18, 1998, 3:00:00 AM5/18/98

to

>On Mon, 18 May 1998, Andrew M. Duncan wrote:

>

>> I'm looking for a few number-theoretical properties of 38 -- my upcoming

>> age.

How about: the sum of the squares of 38's prime factors

equals the number of days 38 will BE your age.

-Xcott

May 19, 1998, 3:00:00 AM5/19/98

to

In article <356062...@cs.ucsb.edu>, "Andrew M. Duncan"

<adu...@cs.ucsb.edu> wrote:

> I'm looking for a few number-theoretical properties of 38

It's the largest even number that can't be written as the sum of two

odd composites.

It's the magic constant in the order three magic hexagon (which uses

the numbers 1 through 19).

There may be more in le Lionnais, Les Nombres Remarquables, a book to

which, alas, I do not have access.

Gerry Myerson (ge...@mpce.mq.edu.au)

May 19, 1998, 3:00:00 AM5/19/98

to

In article <gerry-19059...@abinitio.mpce.mq.edu.au>,

I don't have access to that book any longer either, but , if I remember

well, it gives for properties of 38 only the magic hexagonal constant, with a

nice anecdote (it is the *only* magical hexagon possible, and this hexagon is

extremely hard to find by hand; the discoverer spend about 25 years on

it...). More to the point, 39 is the first integer in that book with no

interesting properties known (which makes it , obviously, quite interesting

:-))

-----== Posted via Deja News, The Leader in Internet Discussion ==-----

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May 19, 1998, 3:00:00 AM5/19/98

to

:All:

:

:I'm looking for a few number-theoretical properties of 38 -- my upcoming

:age. You know: the smallest number that..., the only number for

:which..., etc. There is a well-known proof that there are no

:uninteresting numbers. Any suggestions, or pointers to Internet

:resources? Thanks!

:

:Andrew Duncan

:http://www.cs.ucsb.edu/~aduncan

:

:I'm looking for a few number-theoretical properties of 38 -- my upcoming

:age. You know: the smallest number that..., the only number for

:which..., etc. There is a well-known proof that there are no

:uninteresting numbers. Any suggestions, or pointers to Internet

:resources? Thanks!

:Andrew Duncan

:http://www.cs.ucsb.edu/~aduncan

Wait one more year and you will be as old as Jack Benny ... forever :-)

Reference:

Joe Franklin's Encyclopedia of Comedians, p. 51 &ff.

Bell Publishing Co., New York 1985

ISBN 0-517-467658

Happy birthday, ZVK (Slavek).

May 19, 1998, 3:00:00 AM5/19/98

to

In article <356062...@cs.ucsb.edu>,

Andrew M. Duncan <adu...@cs.ucsb.edu> wrote:

:All:

:

:I'm looking for a few number-theoretical properties of 38 -- my upcoming

:age. You know: the smallest number that..., the only number for

:which..., etc. There is a well-known proof that there are no

:uninteresting numbers. Any suggestions, or pointers to Internet

:resources? Thanks!

:

:Andrew Duncan

This may be the only time the square of your age will end with 444.

(Unless you find a wonder drug to prolong your life by 500 years.)

Cheers, ZVK (Slavek).

May 20, 1998, 3:00:00 AM5/20/98

to

On Tue, 19 May 1998 06:27:32 GMT, feld...@bsi.fr wrote:

>More to the point, 39 is the first integer in that book with no

>interesting properties known (which makes it , obviously, quite interesting

>:-))

Which of course, is the crux of the proof of the assertion that there

are not non-interesting numbers...

Jon Press

May 20, 1998, 3:00:00 AM5/20/98

to

On 19 May 1998, Zdislav V. Kovarik wrote:

> This may be the only time the square of your age will end with 444.

> (Unless you find a wonder drug to prolong your life by 500 years.)

462^2 = 213444

May 20, 1998, 3:00:00 AM5/20/98

to

In article <Pine.OSF.3.96.980520...@alsek.maths>,

Jan Kristian Haugland <haug...@maths.ox.ac.uk> wrote:

:

My oversight. Thanks.

ZVK (Slavek).

May 21, 1998, 3:00:00 AM5/21/98

to

The proof only shows that there are no uninteresting *integers*.

As I've pointed out before, there are many uninteresting numbers,

Old article follows:

----------------------------------------------------------------

It is a delightful fact that there *is* an uninteresting real number.

Liouville's number is not interesting; it possesses no properties of

interest. It is

infinity

------

\ 1

\ ---- =~ 0.11000100000000000000000100000000000.....

/ k!

/ 10

------

k = 1

It comes out of Liouville's construction of transcendental numbers,

but it was neither the first nor the simplest such number constructed;

the construction evidently generates many other similar numbers in the

same way (for example by replacing 10 with 2, or replacing n! with

some other function such as exp(n) or floor(n^3 log n),) and so

Liouville's number is not even of historical interest. Its sole

constructed property, transcendentality, is shared with almost all

other numbers, and so is not an interesting property of real numbers.

Furthermore, Liouville's Number is not the smallest uninteresting real

number, as there are many other numbers equally uninteresting that are

both smaller and larger. Finally, although it would be rather

interesting if someone were to prove that Liouville's Number were the

*most* uninteresting real number, this is unlikely to occur.

May 21, 1998, 3:00:00 AM5/21/98

to

But doesn't the fact that Liouville's number is the first *provably

uninteresting* number show that it is interesting (in a

meta-mathematical way)?!

Surely, for the standard proof that all positive integers are interesting,

a number is only half as interesting for being the first non-interesting

case... Assign a "level of interest" I(n) to the positive integer n such

that I(n) = 1 for truly interesting numbers, then (recusively)

I(n) = (1/2) * I(n-1) for all other numbers.

Exercise: what is I(38)?

John Wilson.

On 21 May 1998, Mark-Jason Dominus wrote:

> It is a delightful fact that there *is* an uninteresting real number.

> Liouville's number is not interesting; it possesses no properties of

> interest.

[snip]

May 21, 1998, 3:00:00 AM5/21/98

to

On Wed, 20 May 1998, Richard Carr wrote:

> On Wed, 20 May 1998, Daniel Giaimo wrote:

>

> :Jan Kristian Haugland wrote in message ...

> :>38 is THE ONLY positive integer n with the property that all

> :>digits from 0 to 9 appear among the first 10 decimals after

> :>comma in 1 / n :

> :>

> :> 1 / 38 = 0.0263157894...

> :>

> :

> : Can you prove this?

> :

>

> It can't be too hard to prove. First note that if n>100, the first 2

> places after the decimal point are 00, which narrows down the field of

> candidates considerably and makes checking the rest fairly easy.

And I did actually check ALL integers up to 100. :-)

May 21, 1998, 3:00:00 AM5/21/98

to

Mark-Jason Dominus wrote in message <6k0frn$2pc$1...@monet.op.net>...

>

>In article <356231e6...@news.ne.mediaone.net>, <jep...@aol.com> wrote:

>>On Tue, 19 May 1998 06:27:32 GMT, feld...@bsi.fr wrote:

>>Which of course, is the crux of the proof of the assertion that there

>>are not non-interesting numbers...

>

>The proof only shows that there are no uninteresting *integers*.

>

But you can extend the proof to any set of numbers as long as you accept the

axiom of choice.

--

--Daniel Giaimo

Remove nospam. from my address to e-mail me. | rgiaimo@(nospam.)ix.netcom.com

^^^^^^^^^<-(Remove)

--------------------------------------------------------------------------------

"In a race between a rock and a pig, don't varnish your clams."

--A Wise Elbonian

May 22, 1998, 3:00:00 AM5/22/98

to

> I'm looking for a few number-theoretical properties of 38

-- my upcoming age.

this isn't number-theory, but ~10 days after your

38th birthday, you'll pass your 20,000,000th minute,

and 8 mos later, you'll pass your 5^13 second.

also, you already passed:

your 3^19 th second when you were 36y 10m,

your 2^30 th second when you were 34y 9d,

your billionth second when you were 31y 8m,

your 10,000th day when you were 27y 4m,

your 3^3 rd year when you were 27y 0m,

your e^pi th year when you were 23y 1m,

your 4^4 th month when you were 21y 4m,

your 12! th second when you were 15y 2m,

your 7! th day when you were 13y 9m,

and you will pass:

your 10! th hour when you're 41y 4m,

your e^2pi th month when you're 44y 7m,

your 6! th month when you're 60y 0m,

your 5^5 th week when you're 60y 1m,

your 7^11 th second when you're 62y 7m,

your 12^7 th minute when you're 68y 1m,

your 11^9 th second when you're 74y 8m,

your 7^9 th minute when you're 76y 8m,

your 7^7 th hour when you're 93y 11m,

your 7! th week when you're 96y 11m,

your 8! th day when you're 110y 4m,

your millionth hour when you're 114y

so, being 38 years old is kind of special, in that

your age is unusually close to a large round-number

interval: 20,000,000 minutes.

- don davis, boston

May 22, 1998, 3:00:00 AM5/22/98

to

In article <6k1opd$d...@sjx-ixn8.ix.netcom.com>, "Daniel Giaimo"

<rgi...@nospam.ix.netcom.com> writes:

>>The proof only shows that there are no uninteresting *integers*.

>

> But you can extend the proof to any set of numbers as long as you accept

>the axiom of choice.

The proof that there are no uninteresting integers extends with no modification

to show that there are no uninteresting ordinal numbers, since if there were

any,

there would be a least one. However, this only shows that all real numbers are

interesting if we assume that there is an interesting well-ordering of the

reals,

doesn't it? And we may doubt this, even if we believe that there exist

well-orderings of the reals, and even that they are collectively interesting.

Keith Ramsay "Thou Shalt not hunt statistical significance with

kra...@aol.com a shotgun." --Michael Driscoll's 1st commandment

May 23, 1998, 3:00:00 AM5/23/98

to

In article <Pine.LNX.3.96.98052...@another-world.maths>,

John Wilson <wil...@maths.ox.ac.uk> wrote:

>But doesn't the fact that Liouville's number is the first *provably

>uninteresting* number show that it is interesting (in a

>meta-mathematical way)?!

If it were, it might, but it isn't, so it doesn't.

May 24, 1998, 3:00:00 AM5/24/98

to

> I'm looking for a few number-theoretical properties of 38 --

Take the cube of 38 :

38^3 = 54872

Convert 54872 to base 9 and one gets 83238 !

1) 83238 is a nice palindrome.

2) 83238 ends with ...38 ! The circle is closed.

--

Patrick De Geest

[mailto:Patrick...@ping.be]

---------------------------------------------------

URL : http://www.ping.be/~ping6758/index.shtml

---------------------------------------------------

May 25, 1998, 3:00:00 AM5/25/98

to

In article <ddavis-2205...@10.0.2.15>, dda...@openmarket.com (don

davis) wrote:

=> In article <356062...@cs.ucsb.edu>, "Andrew M. Duncan"

=> <adu...@cs.ucsb.edu> wrote:

=>

=> > I'm looking for a few number-theoretical properties of 38

=> -- my upcoming age.

=>

=> you already passed:

=>

=> your 10,000th day when you were 27y 4m

I threw myself a birthhour party when I reached my 10000th day.

Gerry Myerson (ge...@mpce.mq.edu.au)

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