Favourite numbers

In this note, you can tell everyone about your favourite number.

The number should have some interesting property which makes it your favourite.

Note : your number should be a natural number

.

#NumberTheory

Note by Mr. India
2 years, 1 month ago

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1 vote

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Comments

My favourite number is 142857142857

It is a cyclic number

It is a kaprekar number

It is a harshad number

17=0.142857\frac{1}{7}=0.\overline{142857} and interestingly, 1142857=0.000007\frac{1}{142857}=0.\overline{000007}

142+857=999142+857=999 and 14+28+57=9914+28+57=99

Mr. India - 2 years, 1 month ago

My favorite number is 46793077744679307774. It has 1010 digits, and it you sum each digit raised to the 1010th power (e.g. 410+610+710+910+310+010+710+710+710+4104^{10}+6^{10}+7^{10}+9^{10}+3^{10}+0^{10}+7^{10}+7^{10}+7^{10}+4^{10}), you will get 46793077744679307774, the same number.

Joshua Lowrance - 2 years, 1 month ago

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Interesting!!

Mr. India - 2 years, 1 month ago

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Are there any other numbers with similar property?

Mr. India - 2 years, 1 month ago

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@Mr. India Yes. View this oeis page.

Joshua Lowrance - 2 years, 1 month ago

Does such a number exists in every base ? So in base n a n-digit number with is the same as raise the digits to n and add up these numbers.

CodeCrafter 1 - 2 years, 1 month ago

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That is a really interesting question, to which I have no answer. I would definitely love to look into this more, though.

Joshua Lowrance - 2 years, 1 month ago

this page has numbers for different bases

Mr. India - 2 years, 1 month ago

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@Mr. India Thanks so much!!

Joshua Lowrance - 2 years, 1 month ago

73 and 42.

73 is the 21th prime number

21=7321 = 7 * 3

37 is the 12th prime number(Do you see the symmetry).

73 is in base 2 1001001 which is symmetric.

42 is coolest of each number(hopefully you know why, if you don't know why, don't panic ).

CodeCrafter 1 - 2 years, 1 month ago

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Nice symmetry. And yes, 42 is the supreme number. Don't forget your towel!

Joshua Lowrance - 2 years, 1 month ago

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42 is so fly, I accidentally missed the ground

Dan Woldeyesus - 2 years, 1 month ago

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@Dan Woldeyesus please please please tell me why 42 is so great

Mary Brown - 2 years, 1 month ago

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@Mary Brown Read the "The Hitchhiker's Guide to the Galaxy" book and you will understand everything. Sometimes it is a litte bit confusion, but it is still a essential book for people who do something with math (why? I don't know).

In other words 42 is a random number, which a random guy wrote in a random book, and it is the answer of life, universe and everything, and that's why it is so special.

CodeCrafter 1 - 2 years, 1 month ago

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@CodeCrafter 1 42 is not a simple random number. There are a number of properties for which, it is the first or the last know number having them. And at least for one:

"42 is the only known value that is the number of sets of four distinct positive integers a, b, c, d, each less than the value itself, such that ab − cd, ac − bd, and ad − bc are each multiples of the value. Whether there are other values remains an open question."

Quoted from the Wikipedia.

João Pedro Afonso - 2 years, 1 month ago

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@João Pedro Afonso Cool properties... But for Douglas Adams was 42 still a random number.

CodeCrafter 1 - 2 years, 1 month ago

@CodeCrafter 1 Actually I loved the bits of The Hitchhiker's Guide to the Galaxy, that I heard once on the radio. Forgot about 42 being the answer to everything. Must read it properly. Thanks.

Mary Brown - 2 years, 1 month ago

Reference from big bang theory? :)

Zhang Xiaokang - 2 years, 1 month ago

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Yes ;)

CodeCrafter 1 - 2 years, 1 month ago

Don't laugh, I think my favorite number is 64. My life is full of coincidences related with that number, starting with my birthday year. 6+4=10 is the base of our decimal system, 64 is the 6th power of 2, 6 is the first perfect number and 4 is also a power of 2, 6-4=2, my favorite numerical base, 6*4=24, the number of hours of our day, so, overall, it has a lot of other of my favorite numbers. These is not over the top properties but it is enough to me.

João Pedro Afonso - 2 years, 1 month ago

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I never saw 64 that way.

Mr. India - 2 years, 1 month ago

24 because it is 4!, (2^1)(3^2)(1^3), it is an antiprime, also because of challenge 24, 24 hours in a day, 2+2=4, 2*2=4, 2^2=4, 2^(24-1)=8388608 which is a pretty cool power of 2 since it contains a lot of 8's, and 5^2-1^2, 7^2-5^2.

Ruilin Wang - 1 year, 10 months ago

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Pretty interesting!

Mr. India - 1 year, 10 months ago

Well, my favourite number, even though is kind of cliche, is the Euler Mascheroni Constant!!

I mean it surprises me that we do not have its closed form!!! And this is the kind of number which can be EASILY explained to anyone using its definition, but yet, no one would know the vast amount of properties it has.....!!

Aaghaz Mahajan - 2 years, 1 month ago

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Curious number indeed!

Mr. India - 2 years, 1 month ago

You forgot, it should have be a natural number. I'm not taking it down, I'm sure it must be a very sexy number.

João Pedro Afonso - 2 years, 1 month ago

13, because no one like it

Michael Wang - 2 years, 1 month ago

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Strange reason ;-)

Mr. India - 2 years, 1 month ago

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lol reverse psychology

Michael Wang - 2 years, 1 month ago
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