What's special about this number?

[ultrafilter]

I stumbled across a kinda neat site that lists an interesting property for each positive integer less than 10000. If you like number trivia, check it out.

[Squink]

9052 is the maximum number of regions space can be divided into by 31 spheres.

Woo hoo, my day is made!

[Lord_Ashtar]

It seems like they were really reaching on some of these. For example:

4752 = (4+4)(4+7)(4+5)(4+2).

What’s so special about that?

[Malacandra]

@Lord Ashtar

It seems like they were really reaching on some of these. For example:

4752 = (4+4)(4+7)(4+5)(4+2).

What’s so special about that?

Um, it’s the product of its digits, if you add the same number (4) to each digit. No idea how to prove how unusual that is, but it’s fairly neat.

[MissMossie]

@ultrafilter

I stumbled across a kinda neat site that lists an interesting property for each positive integer less than 10000. If you like number trivia, check it out.

Make that most positive integers. I was born on July 17 and checked to see what was special about 717…appearantly nothing. Maybe I’ll suggest to them that it is the numerical representation of my birthday, so that alone makes it cool.

Thanks for the link though, it’s neat to look at.

[Giles]

@Malacandra

Um, it’s the product of its digits, if you add the same number (4) to each digit. No idea how to prove how unusual that is, but it’s fairly neat.

There are only 2 4-digit numbers of which this is true. The other is:
7744 = (7+4)(7+4)(4+4)(4+4)

With 3, there’s no 4-digit number that works.

With 5:
1500 = (1+5)(5+5)(0+5)(0+5)
3920 = (3+5)(9+5)(2+5)(0+5)

So it looks fairly unusual.

[gotpasswords]

The best they could come up with for 42 is that it’s the fifth Catalan number?

[Lord_Ashtar]

@Malacandra

Um, it’s the product of its digits, if you add the same number (4) to each digit. No idea how to prove how unusual that is, but it’s fairly neat.

I guess I’m just not clever enough to have noticed that.

[Spectre_of_Pithecanthropus]

For 6, I find it interesting that that if you take the differences between any four successive cubes, and then repeat the subtraction three more times, you always end up with 6. I’m doing it with with actual numbers below, the first four cubes, but it works with any consecutive four no matter how large they are.

1----------------------8---------------------27-----------------64

----------7----------------------19-----------------37-------------

---------------------12----------------------18----------------------

-----------------------------------6----------------------------------

[ultrafilter]

@Spectre of Pithecanthropus

For 6, I find it interesting that that if you take the differences between any four successive cubes, and then repeat the subtraction three more times, you always end up with 6. I’m doing it with with actual numbers below, the first four cubes, but it works with any consecutive four no matter how large they are.

1----------------------8---------------------27-----------------64

----------7----------------------19-----------------37-------------

---------------------12----------------------18----------------------

-----------------------------------6----------------------------------

That works because n[sup]3[/sup] is a 3rd-degree polynomial, and therefore the third difference is constant (6 in this case).

[Giles]

@ultrafilter

That works because n[sup]3[/sup] is a 3rd-degree polynomial, and therefore the third difference is constant (6 in this case).

And 6 is 3 factorial (3 x 2 x 1). If you do this with squares, you get a string of 2’s (2 factorial) in the second line. If you do it with fourth powers, you get a string of 24’s (4 factorial) in the fourth line. And so on.

[Spectre_of_Pithecanthropus]

@Giles

And 6 is 3 factorial (3 x 2 x 1). If you do this with squares, you get a string of 2’s (2 factorial) in the second line. If you do it with fourth powers, you get a string of 24’s (4 factorial) in the fourth line. And so on.

Interesting! I was able to do the algebra with general cubes, but I didn’t know the underlying principle.

[cmkeller]

gotpasswords:

The best they could come up with for 42 is that it’s the fifth Catalan number?

Well, it’s not like they know what question it’s the answer to.

[Malacandra]

@cmkeller

gotpasswords:

Well, it’s not like they know what question it’s the answer to.

:: gefillte troutslap ::

[Napier]

>That works because n3 is a 3rd-degree polynomial, and therefore the third difference is constant (6 in this case).

This is the principle behind Babbage’s engine, isn’t it?