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 Post subject: Autobiographical NumbersPosted: 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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 Post subject: Posted: 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 .

Assume

So for some .

This implies that each of .

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

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 Post subject: Re: Autobiographical NumbersPosted: Wed, 2 Dec 2009 21:12:41 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15246
Location: Austin, TX
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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 Post subject: Number of "Numbers" Greater Than NinePosted: 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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 Post subject: Perfect Autobiographical Numbers ?Posted: Sat, 5 Dec 2009 01:03:05 UTC
Another Challenge / Question that I'm curious about.

Would perfect autobiographical numbers exist?

v/r,

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 Post subject: Re: Perfect Autobiographical Numbers ?Posted: Tue, 19 Oct 2010 05:51:58 UTC
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Joined: Tue, 19 Oct 2010 05:14:49 UTC
Posts: 1
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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 Post subject: Posted: Tue, 19 Oct 2010 06:32:49 UTC

Joined: Sat, 26 Apr 2003 22:14:40 UTC
Posts: 2154
Location: El Paso TX (USA)
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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