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 Post subject: Autobiographical Numbers
PostPosted: Wed, 2 Dec 2009 19:42:25 UTC 
Autobiographical numbers are numbers where the first digit tells how many zeros are in the number, the next digit how many ones, and so on.

e.g. 1210 is the smallest autobiographical number.

My question is do prime autobiographical numbers exist? and if so what is the smallest one?

I don't know the answer, and I'm not a mathematician.

v/r,


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PostPosted: Wed, 2 Dec 2009 20:25:45 UTC 
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A little like Sudoku. There are no primes. In fact, all autobiographical numbers must end in zero.

Label the digits x_0, x_1, ..., x_n.

Assume x_n \geq 1

So x_i = n for some i.

This implies that each of x_0, x_1, ..., x_{n-1} = i.

But now you have to have at least i 0s, i 1s, i 2s,...

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PostPosted: Wed, 2 Dec 2009 21:12:41 UTC 
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Casdan1 wrote:
Autobiographical numbers are numbers where the first digit tells how many zeros are in the number, the next digit how many ones, and so on.

e.g. 1210 is the smallest autobiographical number.

My question is do prime autobiographical numbers exist? and if so what is the smallest one?

I don't know the answer, and I'm not a mathematician.

v/r,


I assume you don't allow number of "numbers" where the "numbers" takes a value larger than 9.

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PostPosted: Sat, 5 Dec 2009 01:00:58 UTC 
I don't know. That's a very good question.

I'm not to familiar with these objects, so I'll have to assume that your constraint is correct.


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PostPosted: Sat, 5 Dec 2009 01:03:05 UTC 
Another Challenge / Question that I'm curious about.

Would perfect autobiographical numbers exist?

again, I'm just curious and asking. I don't know the answer.

v/r,


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PostPosted: Tue, 19 Oct 2010 05:51:58 UTC 
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Anonymous wrote:
Would perfect autobiographical numbers exist?

No! There is only a limited number of autobiographical numbers. No perfect numbers among them :-(


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PostPosted: Tue, 19 Oct 2010 06:32:49 UTC 
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In fact there are seven:

1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000

(see http://www.research.att.com/~njas/sequences/A046043 )

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