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Post a number with an interesting property

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Rudin
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25 Nov 2015, 7:32 am

I like the OEIS, it is hours of fun. I could probably spend hours looking at integer sequences.

Please post sequences you find fascinating below.


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Rudin
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25 Nov 2015, 7:34 am

A related sequence is the sequence of numbers n such that 7^n-8 is prime.

282,475,241 is a prime number. In fact here is the entire sequence:

2, 4, 8, 10, 50, 106, 182, 293, 964, 1108, 1654, 1756, 4601, 8870, 15100, 17446, 22742, 34570, 50150, 95276

It is A217131.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Earthling
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25 Nov 2015, 8:03 am

Rudin wrote:
2520

It is divisible by all the numbers from 1 to 10.

How did you find that out?

(DIVISIBLE BY 1, 2, 3...n)=smallest number that can do that
(2)=2
(3)=6
(4)=12
(5)=60
(6)=60
(7)=420
(8)=840
(9)=2520
(10)=2520
(11)=27720
(12)=27720
(13)=360360
(14)=360360
(15)=360360
(16)=720720
etc.



Rudin
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25 Nov 2015, 6:09 pm

Earthling wrote:
Rudin wrote:
2520

It is divisible by all the numbers from 1 to 10.

How did you find that out?

(DIVISIBLE BY 1, 2, 3...n)=smallest number that can do that
(2)=2
(3)=6
(4)=12
(5)=60
(6)=60
(7)=420
(8)=840
(9)=2520
(10)=2520
(11)=27720
(12)=27720
(13)=360360
(14)=360360
(15)=360360
(16)=720720
etc.


I'll give you a hint. There is a special trick for calculating the LCM.

Take 72 and 4

72=3x3x2x2x2
4= 2x2


Do you see that group of two twos? We'll only represent two once.

We'll get 3x3x2x2x2=72.

Now apply that method to all the numbers between 1 and 10.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Earthling
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25 Nov 2015, 7:06 pm

Rudin wrote:
I'll give you a hint. There is a special trick for calculating the LCM.

Take 72 and 4

72=3x3x2x2x2
4= 2x2


Do you see that group of two twos? We'll only represent two once.

We'll get 3x3x2x2x2=72.

Now apply that method to all the numbers between 1 and 10.

I don't clearly understand what you did there. It's the same thing as above.

But I think I understand the overall concept.
You seperate every number from 1-10 into multiplication of smallest primes (possible because every number can be written as multiple of primes) and then you write a multiplication that contains all the terms that you set up from 1-10. But you check that you don't accidentally include multiples that you already have. When you solve this multiplication you get 2520.
Is it that?



Rudin
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25 Nov 2015, 7:17 pm

Earthling wrote:
Rudin wrote:
I'll give you a hint. There is a special trick for calculating the LCM.

Take 72 and 4

72=3x3x2x2x2
4= 2x2


Do you see that group of two twos? We'll only represent two once.

We'll get 3x3x2x2x2=72.

Now apply that method to all the numbers between 1 and 10.

I don't clearly understand what you did there. It's the same thing as above.

But I think I understand the overall concept.
You seperate every number from 1-10 into multiplication of smallest primes (possible because every number can be written as multiple of primes) and then you write a multiplication that contains all the terms that you set up from 1-10. But you check that you don't accidentally include multiples that you already have. When you solve this multiplication you get 2520.
Is it that?


Yes.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


kraftiekortie
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25 Nov 2015, 7:26 pm

Why is 153 known as the Narcissistic Number?



naturalplastic
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25 Nov 2015, 7:46 pm

Rudin wrote:
153=1^3+5^3+3^3

.


For this reason. ^

Its equal to 1 cubed plus 5 cubed plus 3 cubed.



Earthling
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25 Nov 2015, 7:55 pm

Rudin wrote:
Earthling wrote:
Is it that?


Yes.

:D



kraftiekortie
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25 Nov 2015, 8:01 pm

Thanks very much.



Rudin
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25 Nov 2015, 8:22 pm

kraftiekortie wrote:
Why is 153 known as the Narcissistic Number?


Happy 17,900 posts!

It is good to see someone new here. It is usually me, slave, SSV, Adamantium, Earthling and natural plastic.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


kraftiekortie
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25 Nov 2015, 8:25 pm

That's because they are the Math Mavens!

I could have become one myself, actually LOL......but Fate decided otherwise.



Earthling
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25 Nov 2015, 8:46 pm

Rudin wrote:
12=sqrt(4)*(4!/4)+4

sqrt(4)*(4!/4)+4=2*6+4=16

sqrt(4+4+4+4) = 4



Rudin
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25 Nov 2015, 8:57 pm

Earthling wrote:
Rudin wrote:
12=sqrt(4)*(4!/4)+4

sqrt(4)*(4!/4)+4=2*6+4=16

sqrt(4+4+4+4) = 4


Oh yes.

12=sqrt(4x4)x4-4


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Earthling
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25 Nov 2015, 9:10 pm

Adamantium wrote:
Rudin wrote:
20=4!-4+(4-4)


Nice.

With my preference for exponents, I offer as an alternative

(4!-4)^(4/4)=20

I propose this alternative: sqrt(4^sqrt(4*4))+4 = 20



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25 Nov 2015, 9:13 pm

4!-4+4/4 = 21