# 38 not interesting?

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### Andrew M. Duncan

May 18, 1998, 3:00:00 AM5/18/98
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

### Jan Kristian Haugland

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!

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.

### Jan Kristian Haugland

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.

### Jan Kristian Haugland

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...

### Xcott Craver

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

### Gerry Myerson

May 19, 1998, 3:00:00 AM5/19/98
to

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

> 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)

### feld...@bsi.fr

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
:-))

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### Zdislav V. Kovarik

May 19, 1998, 3:00:00 AM5/19/98
to

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

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).

### Zdislav V. Kovarik

May 19, 1998, 3:00:00 AM5/19/98
to

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

### jep...@aol.com

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

### Jan Kristian Haugland

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

### Zdislav V. Kovarik

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).

### Mark-Jason Dominus

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.

### John Wilson

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]

### Jan Kristian Haugland

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. :-)

### Daniel Giaimo

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

### don davis

May 22, 1998, 3:00:00 AM5/22/98
to

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

> 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.

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

### KRamsay

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

### Mark-Jason Dominus

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.

### Patrick De Geest

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

### Gerry Myerson

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